ML19350C143
| ML19350C143 | |
| Person / Time | |
|---|---|
| Site: | Vermont Yankee File:NorthStar Vermont Yankee icon.png |
| Issue date: | 03/24/1981 |
| From: | Pilat E, Slifer B, Verplanck D YANKEE ATOMIC ELECTRIC CO. |
| To: | |
| Shared Package | |
| ML19350C138 | List: |
| References | |
| YAEC-1238, NUDOCS 8103310214 | |
| Download: ML19350C143 (137) | |
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I i METHODS FOR THE ANALYSIS OF BOILING WATER REACTORS STEADY STATE CORE PHYSICS I ' I I I Prepared By: &J h 27 8 D. "M. Ve rPlanck (Date) I Specialist Reviewed By: .
'3/ (Dfite)
R [/ E. E. Fi'lat Manager, Applied Methods Development Approved By: . I g " B. Slifer (Date) W Manager, Nuclear ngineering Dept. Yankee Atomic Electric Company j Nuclear Services Division 1671 Worcester Road ' Framingham, Massachusetts 01701 I I 8108310214
I I I DISCLAIMER OF RESPONSIBILITY This document was prepared by Yankee Atomic Electric Company on I behalf of Vermont Yankee Nuclear Power Corporation. This document is believed to be completely true and accurate to the best of our knowledge and information. It is authorized for use specifically by Yankee Atomic Electric Company, Vermont Yankee Nuclear Power Corporation and/or the appropriate subdivisions within the Nuclear Regulatory Commission only. I 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 warranty or representation with respect to the contents of this document I or to its accuracy or completeness. I I I I l I lI lI I g -u-
I I ABSTRACT This report describes the SIMULATE computer program and models used I by YAEC for steady state BWR core calculations. It provides bases for confidence through comparisons with seven cycles of Vermont Yankee operating data, two cycles of Quad Cities operating data (including gamma scans) and higher order calculations. I I I 'I 'I I I l I I I I -"*- I
I TABLE OF CONTENTS Page DISCLAIMER 11 ABSTRACT ill TABLE OF CONTENTS iv LIST OF FIGURES vi LIST OF TABLES xi ACKNOWLEDGEMENTS xii 1
SUMMARY
l 2 DESCRIPTION OF THE SIMULATE PROGRAM 2 2.1 Geometry 4 4 8 2.2 Neutronics 2.2.1 Cross Sections 4 2.2.1.1 Macroscopic Cross Section Input 5 2.2.1.2 Microscopic Cross Section Input 6 2.2.1.3 Two Group Input Method 6 2.2.2 Internodal Neutron Transport 7 2.2.3 Thermal Leakage Correction 11 2.2.3.1 Internodal Thermal Leakage 11 2.2.3.2 Core Boundary Thermal Leakage 12 2.2.4 Albedos 12 2.2.5 Computation of Nodal Fluxes and Conversion of Source Distribution to Power Distribution 13 t I 2.2.6 The Depletion System 14 2.2.6.1 Depletion of Exposure and History Arrays 15 l I 2.2.6.2 2.2.6.3 2.2.6.4 Nuclide Depletion Equations The Haling Iteration Step Average Depletion 16 17 17 I I
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I I I TABLE OF CONTENTS (Continued) Page I 2.3 Thermal-Hydraulics 18 I 2.3.1 2.3.2 2.3.3 Void-Quality Relationships Leakage Flow and Bypass Voiding Core Inlet Subcooling and Heat Balance 20 21 21 2.3.4 Pressure Drop 22 2.4 The Coupled Nuclear-Hydraulic Iterations 22 3 BASIS FOR CONFIDENCE 30 3.1 Summary 30 I 3.2 Description of the Cores Modeled 3.3 Features of the SIMULATE Core Models 30 31 31 I 3.3.1 3.3.2 3.3.3 Geometry Models Neutronics Models Thermal-Hydraulics Models 31 32 3.4 Comparisons with Data Measured at Vermont Yankee 32 Cycles 1-7 3.4.1 Hot Eigenvalues 32 ll 3.4.2 Flux and Burnup Distributions in the Coy 33 lW 33 l 3.4.3 Cold Criticals 3.5 Comparisons with Data Measured at Quad Cities 34 i Cycles 1-2 3.6 Comparisons with Higher Order Calculations 34 1 3.6.1 Few Assembly PDQ Calculations 35 3.6.2 35 Quarter Core PDQ Calculations 1 i I lI .I
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I I LIST OF FIGURES 2.1 Overall Flow Chart of the SIMULATE Program 25 2.2 Control Volumes and Flows for the BWR Heat Balance 26 2.3 Coupled Nuclear-Hydraulic Iterations 27 3.1 Layout of the Vermont Yankee Core 36 3.2 Layout of the Quad Cities Unit One Core 37 3.3 Vermont Yankee Cycles 1-7, Percent of Core Power vs. Core Total Exposure 38 I 3.4 Vermont Yankee Cycles 1-7, Percent of Core Flow vs. Core Total Exposure 39 Vermont Yankee Cycles 1-7, Relative Water Density vs. Core Total I 3.5 Exposure 40 3.6 Vermont Yankee Cycles 1-7, Control Rod Notches Inserted vs. Core I 3.7 Total Exposure Vermont Yankee Cycles 1-7, Inlet Subcooling vs. Core Total 41 41 Exposure 3.8 Vermont Yankee Cycles 1-7, Calculated K-Ef fective vs. Core Total Exposure 43 l l 3.9 Vermont Yankee Cycles 1-7, Calculated K-Effective vs. Core 44 Average Exposure Core Average Axial TIP Traces, VY Cycle 1, BOC 45
= 3.10 Core. Average Axial TIP Traces, VY Cycle 1, MOC 46 3.11 Core Average Axial TIP Traces, VY Cycle 1, EOC 47 l 3.12 I
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I l I : I p ST OF FICURES (Continued) Page 3.13 Core Average Axial TIP Traces, VY Cycle 2, BOC 48 3.14 Core Average Axial TIP Traceci, VY Cycle 2, MOC 49 3.15 Core Average Axial TIP Traces, VY Cycle 2, EOC 50 3.16 Core Average Axial TIP Traces, VY Cycle 3, BOC 51 3.17 Core Average Axial TIP Traces, VY Cycle 3, MOC 52 3.18 Core Average Axial TIP Traces, VY Cycle 3, EOC 53 3.19 Core Average Axial TIP Traces, VY Cycle 4, BOC 54 3.20 Core Average Axial TIP Traces, VY Cycle 4, MOC 55 3.21 Core Average Axial TIP Traces, VY Cycle 4, EOC 56 3.22 Core Average Axial TIP Traces, VY Cycle 5, BOC 57 3.23 Core Average Axial TIP Traces, VY Cycle 5, MOC 58 3.24 Core Average Axial TIP Traces, VY Cycle 5, E0C 59 3.25 Core Average Axial TIP Traces, VY Cycle 6, BOC 60 3.26 Core Average Axial TIP Traces, VY Cycle 6, MOC 61 3.27 Core Average Axial TIP Traces, VY Cycle 6, EOC 62 ,_I 3.28 Core Average Axial TIP Traces, VY Cycle 7, BOC 63 3.29 Core Average Axial TIP Traces, VY Cycle 7, MOC 64 3.30 Core Average Axial TIP Traces, VY Cycle 7, EOC 65
.3.31 Unnomalized TIP Traces, VY Cycle 1, BOC 66 3.32 Unnormalized TIP Traces, VY Cycle 1, MOC 67 3.33 Unnomalized TIP Traces, VY Cycle 1, EOC 68 3.34 Unnormalized TIP Traces, VY Cycle 2, BOC 69
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r I I I LIST OF FIGURES (Continued) i Page Unnormalized TIP Traces, VY Cycle 2, MOC 70 3.35 3.36 Unnormalized TIP Traces, VY Cycle 2, EOC 71 3.37 Unnormalized TIP Traces, VY Cycle 3, BOC 72 l Unnormalized TIP Traces, VY Cycle 3, MOC 73 3.38 Unnormalized TIP Traces, VY Cycle 3, EOC 74 lg 3.39 ,g 3.40 Unnomalized TIP Traces, VY Cycle 4, BOC 75 Unnormalized TIP Traces, VY Cycle 4, MOC 76 3.41 Unnormalized TIP Traces, VY Cycle 4, EOC 77 3.42 Unn .rmalized TIP Traces, VY Cycle 5, BOC 78 ! 3.43 Unnormalized TIP Traces, VY Cycle 5, MOC 79 3.44 Unnormalized TIP Traces, VY Cycle 5, EOC 80 3.45 1 Unnormalized TIP Traces, VY Cycle 6, BOC 81 3.46 Unnormalized TIP Traces, VY Cycle 6, MOC 82 3.47 Unnormalized TIP Traces, VY Cycle 6, EOC 83 3.48 Unnormalized TIP Traces, VY Cycle 7, BOC 84 3.49 l8 l 3.50 Unnormalized TIP Traces. VY Cycle 7, MOC 85 Unnormalized TIP Traces, VY Cycle 7. EOC 86 l 3.51 3.52 VY Cycle 1 Comparison of SIMULATE and Process Computer EOC Bundle Average Exposures 87 3.53 VY Cycle 2 Comparison of SIMULATE and Process Computer EOC Bundle Average Exposures 88 J 3.54 VY Cycle 3 Comparison of SIMULATE and Process Computer EOC Bundle Average Exposures 89 I
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I I LIST OF FICURES (Lontinued) Page I 3.55 VY Cycle 4 Comparison of SIMULATE and Process Computer EOC Bundle Average Exposures 90 3.56 VY Cycle 5 Comparison of SIMULATE and Process Computer EOC Bundle Average Exposures 91 3.57 VY Cycle 6 Comparison of SIMULATE and Process Computer EOC Bundle Average Exposures 92 I 3.58 VY Cycle 7 Comparison of SIMULATE and Process Computer EOC Bundle Average Exposures 93 I 3.59 Quad Cities Cycles 1-2, Percent of Core Power vs. Core Average Exposure 94 3.60 Quad Cities Cycles 1-2, Percent of Core Flow vs. Core I Average Exposure 95 3.61 Quad Cities Cycles 1-2, Control Rod Notches Inserted vs. Core Average Exposure 96 3.62 Quad Cities Cycles 1-2, Relative Water Density vs. Core Average Exposure 97 3.63- Quad Cities Cycles 1-2, Inlet Subcooling vs. Core Average Exposure 98 lI l 3.64 Quad Cities Cycles 1-2, K Effective vs. Core Average Exposure 99 3.65 Quad Cities Core Average Axial TIP Traces, Cycle 1, BOC 100 l 3.66 Quad Cities Core Average Axial TIP Traces, Cycle 1, MOC 101 3.67 Quad Cities Core Average Axial TIP Traces, Cycle 1, EOC 102 3.68 Quad Cities Core Average Axial TIP Traces, Cycle 2, BOC 103 3.69 Quad Cities Core Average Axial TIP Traces, Cycle 2, MOC 104 3.70 Quad Cities Core Average Axial TIP Traces, Cycle 2, EOC 105 3.71 Unnormalized TIP Traces QC Cycle 1, BOC 106 , 3.72 Unnormalized TIP Traces, QC Cycle 1, MOC 107
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I I LIST OF FIGURES (Continued) Page Unnormalized TIP Traces, QC Cycle 1, EOC 108 I 3.73 3.74 Unnormalized TIP Traces, QC Cycle 2, BOC 109 3.75 Unnormalized TIP Traces, OC Cycle 2, MOC 110 3.76 Unnormalized TIP Traces, QC Cycle 2, EOC 111 3.77 Quad Cities EOC 2 Assembly Gamma Scan Comparison 112 3.78 Quad Cit 1es EOC 2 Average Axial Gamma Scan Comparison 113 7 3.79 Comparison of Assembly Powers, SIMULATE vs. Heterogeneous PDQ, 3x3 Array 114 I 3.80 Comparison of Assembly Powers, SIMULATE vs. Heterogeneous PDQ, 3x3 Array 115 3.81 Comparison of Assembly Powers, SIMULATE vs. Heterogeneous PDQ, 3x3 Array 116 3.82 Comparison of Assembly Powers, SIMULATE vs. Heterogeneous PDQ, Radial Plane Typical of Bottom of Core 117 l 3.83 Comparison of Assembly Powers, SIMULATE vs. Heterogeneous PDQ, Radial Plane Typical of Core Mid-Plane 118 1 3.84 Comparison of Assembly Powers, SIMULATE vs. I Heterogeneous PDQ, Radial Plane Typical of Top of Core 119 'I I I I
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I I LIST OF TABLES Page 2.1 Independent Variables Available to Cross Section Input Vectors 28 i 2.2 Cross Sections and Basic Equations for the Two Group Input Method 29 3.1 Characteristics of Vermont Yankee and Quad Cities 1 120
- 3. 2- Operating History of Fuel in Vermont Yankee 121 3.3 Results of Vermont Yankee Cold Critical Analyses 122 I
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I I I ACKNOWLEDGEMENTS I The author gratefully acknowledges the assistance of R. A. Woehlke, M. A. Kmetz, J. M. Holzer, M. J. Hebert, G. D. Dooley, G. M. Solan, and N. Mahoney in performing the programming and analyses reported here. Dr. Burt. Zolotar of EPRI was kind enough to supply the void quality correlation. I I I I I 'I I I I lI I I I
I I 1
SUMMARY
I This report describes the codes and models used at Yankee for steady state neutronic analysis of BWR's. Steady state neutronic calculations are carried out primarily with an updated version of the SIMULATE code. Other versions of SIMULATE have been used in PWR analysis (18) and part of the development work has been sponsored by EPRI(1). I The core is modeled using nodes which are approximately six-inch cubes. Two group macroscopic cross sections from CASM0(19) analyses of I single bundles are used to characterize the node average neutronic properties as a function of local nodal conditions (exposure, temperature, etc.). Internodal neutron transport is calculated by a modified, one group, coarse r I mesh, dif fusion theory which includes allowance for flux discontinuity factors between nodes. Yankee's BWR core models have been checked against various measurements from Cycles 1-7 of Vermont Yankee and from Cycles 1-2 of Quad Cities Unit 1, and also against higher order benchmark calculations. The I results for 119 statepoints covering the first seven Vermont cycles under a wide variety of operating conditions show: For hot eigenvalues, a total standard deviation of 0.0027; A hot eigenvalue standard deviation of 0.0012 within any one cycle; I - A cold average eigenvalue of 0.989 with a standard deviation of 0.003;
- A standard deviation of 6.4% on the peak to core average TIP trace value.
I I I I I I i I I
I I 2 DESCRIPTION OF THE SIMULATE PROGRAM The SIMULATE program has been developed for three dimensional steady state nodal analysis of light water reactor power distributions. The program I may be applied in studies of reactor cycle length, power distribution, control rod patterns, and xenon transients in either PWR's or BWR's. Earlier versions of the program have been used extensively at Yankee Atomic Electric Company (YAEC) in the period from 1971 to 1977. The present version results I from a de program at YAEC sponsored by the Electric Power Research Institute ((opeent(EPRI) to generalize and document the program suitably for general usage at utility companies. A concurrent development project at I Rensselaer Polytechnic Institute (RPI) sponsored by EPRI contributed to this development program by generalizing the definition and application of the program's original neutron balance equation. The reactor core is represented in SIMULATE u in familiarinnodalsimulationprogramssuchasFLARE(2,gthengdalization TRILUX( ) and others. Either one or four nodes are used per assembly in the horizontal plane and I f rom one to twenty-five may be used vertically. The neutron balance equation is essentially coarse mesh diffusion theory. It is basically a one group method; however, with two group cross sections input, a thermal leakage correction may be calculated internally for each node to provide an approximate two group result. The calculations are executed only in the fuelled area of the core with albedos being used to terminate the neutron balance equation at the core-reflector interfaces. I s The SIMULATE program has a great number of options and features developed over the years to improve and speed its application in reactor I analyses. Features generally have been added: 1) to improve accuracy; 2) to improve the ability to verify the input and output; 3) to provide geometry and boundary condition flexibility; 4) to maintain acceptable run costs; and 5) to include new analytical and optimization capabilities. The program has the following major features:
- 1. Doppler, xenon, and moderator ef fects on the cross sections are
' calculated during the power feedback iteration. Control rod position, i core power, core flow or soluble boron may be adjusted by criticality searches. l 2. Fission product concentrations may be maintained for I, Xe, Pm and Sm and transients may be calculated. Stepwise depletion and the Haling 'lu power-exposure iteration are available.
- 3. Input macroscopic cross section data may be supplied in one or two group formats. The cross section input system is generalized to allow
)obal neutron balance equation interfaces with the cross section I input syst. the primary Hough the one group nodal values of koo , M2 andEt r. Thus,
- t. .jectiveofcrosssectgoninputpreparationistocausethe program to calculate accurate k., M andI~tr values for each node, including the full range of variation of the independent variables in a given case.
The input cross sections are also used in evaluating nodal fluxes ior the fission product depletion equations and the thermal leakage correction. I Cross sections are input using a two group format. Each cross section is fit independently and k. is computed by the code using the formula derived from two group theory. The two group formula tends to account I intrinsically for the cross-coupling of tha many reactivity ef fects involved, for example: control witt. xenon, control with exposure, etc. without complex cross coupling expressions. With the two group format, options are available to internally calculate a correction to the power distribution to account for thermal neutron leakage between nodes of differing composition. This thermal leakage correction may also be used in the calculation of the multiplication kg from the cross sections so that a spectral corrected value I is used to replace ke in the neutron balance equation. 2.2.1.1 Macroscopic Cross Section Input In general, a macroscopic cross section is developed as the summation of several user defined pieces called " partial cross sections",6E ig: I r. = 4f of 1
* * (2.1)
Each of these pieces may be expressed separately by the user using the following function of three variables: 3 6122 = Fu (g) Fu (z) In this equation: I i denotes the cross section type (i.e., absorptien, fission, etc.). I f uniquely identifies each of the " partial cross section" terms (alig) within a fuel type. l x,y,z are chosen from the list of independent variables in Table 2.1. Fi g(x,y) may be a polynomial or interpolating table in x and y or in x alone. 5 I
I I F2t(z) is an optional polynomial in z. 2.2.1.2 Microscopic Cross Section Input In addition to the macroscopic nodal cross sections, microscopic absorption cross sections are needed in the fission product depletion e qua tions . The cross section coding was developed to allow input of a full set of nine two group macroscopic cross sections. Each macro cross section I may be assembled as the sum of several lumped macro portions plus several microscopic contributions by nuclide. Only the depletion equations for iodine, xenon, promethiun and samarium are coded, so only their number I densities are generated during program execution and only their microscopic cross sections are needed. The microscopic cross sections are input in the same way as the macros, and are allowed to have the same range of functional dependencies. 2.2.1.3 Two Group Input Method The two group input method requires the user to provide correlations defining each of the two group dif fusion parameters listed in Table 2.2. All of the independent variables listed in Table 2.1 are available for use I in those correlations. The two group equation is used to define the nodal multiplication constant kg as: y* _ s k + s k 2 (G.1 /$1)
! E.1 + I ,. ( 9 2/9, ) (2.3)
The flux ratio 6 /d is expressed as I 2 l A 1= Y2 4. 2, (2.4) where T is a correction factor which accounts for thermal neutron leakage l !g between nodes. When there is no thermal leakage between nodes, T is unity lg and the flux ratio reverts to its asymptotic value obtained by equating l thermal neutron absorption in the node to thermal neutron source in the node due to slowing down. Substituting Equation (2.4) into Equation (2.3) yields the two group formula for ki: 2 43 k3. Y1 _ ' I- b y2 a,2, - - c.1 Y fl- (2.5) When T is unity, this is the familiar form for k e in two groups. lI Other values needed are computed as follows: 6 'I
I I
~
- 3 t v 1, a.: Yi (2.6)
, w= r + 1/a rm ra m ,, ,,
The one group value of 1 , is collapsed from the two group data: I E= %+TI d/G v + tim /I .J (2.8) I The one group transport cross section is collapsed from the two group data by conserving migration area: I =1(31 M) (2.9) The values of 31 ,k e defined here are fed into the calculationoftheinternoda[andk transport as shown in Section 2.2.2. The values oft ,#1 2' XEf1 and REf2 are used in Sections 2.2.5 in convertinr, the source stri ution S ijk to the power distribution Pgjp. 2.2.2 Internodal Neutron Transport ! Neutron transport between nodes is calculated using the modified coarse mesh diffusion theory equations developed by Borr*sen(4). This is j a variant of the ordinary, coarse mesh diffusion theory familiar in CITATION (5) I and other common computer codes. It can also be developed through the use of the transmission matriv. approach (6J. The neutron balance for node i is written as: huYYe6I iM )-(C UYfe nS out)+ [ Net Source) = 0 (2.10) i I I t J ., - M . p d* EHL z. ; g v =c o j d j 8 - (2 11) where: l j pq
= partial current from node p to adjoining node q;
Atom 1 8 ; I
I I I l where: l I _. pg = average flux in node 1 l l fi = flux at the center of node 1 ([f = represents the fluxes on each of the faces of node i SIMULATE uses the weighting factors given by Borresen:(4) 3A _ 0 _- (2.15) g 3 A + (1- A XR +.0 i- A l t[A + Cl-A)( R +.O] (2.le) I R = h* /k* (2.17) I where: A is input h= node width in radial direction k= node height in axial direction For cubic nodes, which are common in BWR analysis: R=1 B=A C = (1-A)/12 A value of unity for A reduces the calculation to the special case of ordinary coarse mesh dif fusion theory (CMDT). Comparisons of SIMULATE nodal calculations using conventional flux and volume weightsd cross sections with parallel fine mesh heterogeneous I PDQ calculations show substantial flux distribution distortion between controlled assemblies and their neighbors and between assemblies with differing void fractions. The discontinuity factor, f, if different from 1.0, introduces discontinuities in the coarse mesh flux at node interfaces. This factor can correct the nodal reaction rates to agree more closely with i fine mesh heterogeneous reference results. ideallybeappliedseparatelyaneachface(p1thoughthefactorshould,
) Koebke I 9 I
l E 1 I applying one average factor:
"If the outer boundary conditions of the spectral geometry are varied, the averaged cross sections of the embedded region can be approximated as a I linear function of the physical quantities to be conserved:
+
I ~~~ usT
~~
}*, do EG = Eugyfo),
G l
+ $$r -
doV l L c., g; (0) is the cross section for zero total leakage [t.[c,lo in all macro groups. The coefficient matrix can be deduced from Ng + 1 spectral calculations (Ng = number of the macro groups). . . The matrix elements (,(, / ifthecrosssectiondistribution[g""(r) sows I must be taken into account large variations or, if there is a large spectral shift within the region considered. The formula ... should be applied if in a global reactor solution the neutron physics states of the considered region differ I considerably in leakages." In our work, the correction factor, f, defined by: HEY l - . _
~
bgg G ) (2.18) I has been determined by taking Koebke's recommendation literally -- i.e., I by actually performing fine mesh PDQ calculations for the assembly of interest " imbedded" in at least eight neighbors. These are described in more detail in Section 3.6-1. The resulting factors are not determined by integration but by rewriting the definition: asm) 4~ (2 "> lE reasu) lI l where: 'E CASHo) - node average cross section from unit assembly calculation; 10 lI
E I _ h jj h = node average cross section required to provide the correct power distribution and eigenvalue for the SIMULATE calculation of the few bundle problem. For use in the SIMULATE core model, the resulting values of f are characterized as a function of local nodal conditions, just as the cross sections are. I 2.2.3 Thermal Leakage Correction 2.2.3.1 Internodal Thermal Leakage A thermal leakage or supplemental power correction as proposed by I Becker (9) may be computed and applied. Equations appearing in Section 2.2.5 show the usages of the thermal leakage correction factor called T. The thermal leakage correction is available only with two group input. I The purpose of the correction is to account for spatial transients in the thermal flux which occur at the interfaces of nodes having differences in composition. Such transients appear in the vicinity of control rods, poison rods, plutonium assemblies and at the core-reflector interface. Lesser I spatial transients occur at interfaces of similar nodes in checkerboard shuffling patterns. SIMULATE includes optional methods by which the effects of thermal leakage can be included in the calculations. The calculation proceeds as follows: I 1. The global (whole reactor) neutron balance equation is solved as a one group equation using the infinite medium spectrum values for the multiplication (ky, absorption (E,) and transport (ftr) n dal I properties. While two group cross sections must be input, they are collapsed to one group prior to use using the asymptotic (infinite g medium) fast to thermal flux ratio. A global distribution of neutron g source and reactor keff result.
- 2. The amount of thermal neutron leakage into or out of each node is I calculated using a simple one dimensional diffusion theory formula.
Thermal leakage is expressed as a correction factor applied to the asymptotic thermal to fast flux ratio. The calculation is only an estimate and is of adequate accuracy if the nodes are not highly coupled I thermally (thermal leakage less than 5%). It is an approximation using the sum of six separate one dimensional results to represent what are really coupled ef fects of the six neighboring nodes.
- 3. On option, the thermal leakage effect on the global power distribution is determined in one of two ways. At the first level, the final power distribution is calculated from the corrected values of nodal two group I fluxes using XIyy and kT f2 ; reactor k,gg is not affected. At the second level, the neutron balance equation for the next void iteration uses one group properties k, I krcollapsed from the two group input usingthecorrectedtherma$and to fast ratio. Reactor power distribution I and k,gg are affected resulting in an approximate two group result.
I 11 I
I The thermal leakage correction, T, for a node is defined as the I ratio of the corrected thermal flux 0 2T t the asymptotic thermal flux. T= $r 2 (fy, ( /f.2) (2.20) To evaluate T, the four horizontal components j and two vertical components k are summed: y
- 33. -f-T = l + fy,q ((BTLC .q (DX - j:gg, (DZ) - (2.21) where: L = thermal diffusion length in the node A) = coefficient of the exponential transient in the 1-D diffusion theory solution for each face.
The input factor BTLC is included to account for assembly designs which tend to have less horizontal themal communication due to water gaps I or other complex geometry. 2.2.3.2 Core Boundary Thermal Leakage The themal transient at the core-reflector interface is not addressed analytically by the thermal leakage calculation. For nodes along the core-reflector interf ace a thermal return current may be simulated using: ,I AG2 = AA
- G2*M (2.22)
! Here M 2 is the migration area in the peripheral node, and AA is input 2.2.4 Albedos Albedos are used to terminate the SIMULATE nautron balance equation l at the core-reflector interface. Elimination of the reflector from the lg calculation substantially reduces the number of nodes in the calculation g and reduces the accompanying computation and storage difficulties. The albedo needed for input to SIMULATE is U (2.23)
, = Q,i" "U Here Jg out is the one group current leaving the core from node i and Jg h is the one group current returning. Methods are available to calculate albedos for flat interfaces and inside, or outside corner combinations.
Due to the presence of complex geometry in real reactors, however, final normalization may have to be performed. , I E I 12 lI
E l I 2.2.5 Computation of Nodal Fluxes and Conversion of Source Distribution E to Power Distribution The relation between fast and thermal fluxes (either relative or I absolute) is evaluated for each node as: 4 / v, = r I ,., / I m (2.24) where the cross sections are those appropriate to the node of interest, and T is the node-dependent correction factor which accounts for thermal neutron leakage between nodes. When there is no thermal leakage between I nodes, T is unity and the flux ratio reverts to the asymptotic value obtained by equating thermal neutron absorption in the node to thermal neutron source in the node due to slowing down. The neutron source distribution Si g (or simply S) provided by solution of the neutron balance equation is converted first to relative nodal flux distribution, then to relative nodal thermal power distribution, I and then to absolute nodal flux distribution, which is required to solve the nuclide depletion equations: l 4l* = S / C v h , + v E,z l$a /q,D (,,,,, E fl (2.26) I
$^2 C P"/Cx E 4-Xh.1 69 2 /$,3 (2.27) p2 g
where: 4[' = Relative average flux in node (2.28) N= Absolute average flux in node (2.29) C= Conversion factor from relative nodal power to l ( absolute thermal power density in the node, computed as: (PTil)(B) (10-24) / (VOL) (2.30) PTil = The reactor thermal power in FNt for the explicit core. l B= A constant to convert the units of Kappa ()() ' in X'k to FNt-sec. 13 I
E I I g 2/bn. Macroscopic cross sections are in cm-1 10-24 , Microscopic cross sections are in barns (bn). Fluxes Oy and G2 are defined internally in n/bn-sec. VOL = The volume of the explicit core in em 3computed from the core geometry, (i.e., the sum of the volumes of the nodes included in the calculation). Here the fluxes, source, power and cross sections are those appropriate to each node, and the ratiol@y/k is evaluated for each node from Equation I (2.24). After the fast flux has been evaluated in this way from Equations (2.25) and (2.27), the thermal flux itself is recovered from the fast by another application of Equation (2.24). flux 2.2.6 The Depletion System Exposure (E), void history (V) control history (CF) and several I nuclide concentrations (Nn ) are maintained by the program for every reactor node. Initial values of E and V may be established for burned fuel by direct input. Values for the nuclide concentrations may be initialized internally I as zero (0,0) or they may be initialized by way of the power dependent equilibrium equations. Built-in depletion equations are used to update these exposure related variables automatically for every node during depletion time steps. The built-in equations and the control logic involved I are developed in this section. The variables E and V and CF and the concentrations nN are all available for use in the cross section input Cross sections are developed as a lumped macroscopic corralations. I contribution correlated with E and V (etc.) plus the sum of a series of microscopic contributions using the Nn and nicroscopic cross sections. The cross section input portion of the program is written generally I enough to handle many nuclides and each of their microscopic cross sections. At this time, only the nuclide depletion equations for I-135, Xe-135, Pm-149 and Sm-149 are coded. Furthermore, for Pm and Se, only the primary I chain is present. The basic depletion system logic provides the familiar timestep depletion method; the power distribution used is the beginning of step distribution and itThis is held constant for the depletion interval, going f orwa rd in t ime . system is augeented by the following options providing greater flexibility and reducing the number of timesteps needed in some I analyses: fis.
- 1) Automatic equilibrium concentrations for the power dependent products
- 2) The Haling end of cycle power-exposure iteration.
14 I.
E I 3) Depletion with the timestep average power distribution (predictor-corrector type).
- 4) Reverse depletion using a negative exposure interval.
An end of life exposure search causing a depletion case to end at an I 5) input value of k,ff. 2.2.6.1 Depletion of Exposure and History Arrays I The exposure (E), void history (V) and control history (CF) arrays are carried as concentrations in the concentration file. In a normal depletion step, these histories of a node are updated as: ( S -- (2.31) I (ZBON)(M) E : E+ MMC ) (2.32) V' = (E)(v) + (U){ P)(DE)(C ) I E # (2.33) c p': (E)(CF) + (CT)(P)(DE)(C) (2.34) E' where: M= Initial tons of heavy metal per assembly (by fuel type). TONS = Explicit core total of M, computed internally. ZBUN = The number of assemblies in the explicit core, computed I internally. DE = The core average exposure interval in GWD/T. If DE is input in hours, the conversion to GWD/T is made prior to usage: DE' = DE x PTH/(24 x 1000 x TONS) (2.35) where: i PTH = The reactor power. E 15
- I
I 2.2.6.2 Nuclide Depletion Equations The following differential equations govern the concentrations of I-135, Xe-135, Pm-149 and Sm-149 in any node: I 1 i (2.36) l d__Ny = yt - Ar Nr db , MNX= Y - A Nx 4- hr Nr (2.37) Ak" I -- h,o - p _. M P P (2.38) l d N s = y, - p, N, + h , N, (2.39) l ~R~
- bh h + 1 Y Cda a (2.40)
G,02 y are derived in Section 2.2.5 (n/bn-sec) A n = the decay constant (sec~i) for nuclide n N = the number density of nuclide n (atoms /bn-cm) n Yn = the yield rate from fission for nuclide n defined by: _. y )(p $, 4- J/ @a) (2.41) Y n " the yield fraction of nuclide n from fission defined in input
# = neutrons per fission The e9=itibriu= concentrations co=9uted =ader ==er option are the lE 'N solutions of the above equations for dN/dt = 0.0.
I lI e
I When nuclides are depleted from the given number density at the the end of the step N I beginning of the time dependent step N solutions n ( ) to that at (2.36) through (2.39)are of equations n(t), Since the coupled differential equations governing I and Xe are parallel the needed.
; solution for I and Xe is presented to those governing Pm and Sm, only (
here: (;_. g er D N1 (.4 ) : Nr lo) e Ar h-12 Y (2.42) Az I -A *
- Ax A -
Nxl6): NJoM *h+ lo+Adr'r c. l . Ax Ar4x . -l - (2.43) A* l
' Ax E
+ ArNrlo) -
Az Yz r r
-g x -A I Ar(Ax- A 2) . , ~
2.2.6.3 The Haling Iteration The Haling iteration makes continuous reference to the beginning-of-step exposure distribution while converging on a self consistent power and exposure shape for the end of the step. The beginning-of-cycle exposure (and power and concentrations) are placed in the " Haling / Memory / Target" files and are reread at each void iteration. The iteration may be performed in conjunction with the end of life exposure search. Briefly, the Haling iteration solves for the consistent power and incremental exposure distributions at the end of step such that:
- 1. The power distribution is the same as the incremental exposure
.t I distribution: (2.44) E =E +P ijk (DE)(C) and,
- 2. The power distribution Pi jk is the solution obtained at end-The step is a single timestep of length DE involving void iterations I to bring the power and incremental exposure distributions to convergence.
2.2.6.4 Step Average Depletion Depletion steps using the timestep average power distribution are performed. This has been found useful in a depletion of a core having 17
I burnable poison and may improve the accuracy of xenon transient calculations. A special input procedure provides the following sequence automatically:
- 1. Calculate the power distribution PC at the beginning of the step exposure EO.
- 2. Deplete an interval DE to El using P0 .
1
- 3. Calculate the power distribution P at El .
- 4. Redeplete from E to E l using (P + P 1)/2.
- 5. If desired, calculate PI ' at E 'I as the " final answer".
2.3 Ther=al-Hydraulics The objective of the hydraulics calculation is to compute the nodal relative water density array U1 for use in cross section fits. I Calculations are performed for hdividual channels using the local power distribution and channel flow. Individual channel flows are adjusted to obtain identical core pressure drops across all the channels. Thermal-hydraulic feedback is under user control and may be bypassed; when bypassed, the array U gp is set to an input value everywhere in the core. This value may be varied to study isothermal effects. For a EW, I in-channel void f raction is calculated from a correlation and a bypass void calculation may be included. An automatic core inlet subcooling calculation is available. Internal steam tables provide water properties where needed. I Calculations proceed as follows: Core flow is first distributed to the channels using the iterative I 1) procedure to balance assembly pressure drops. ,g 2) The channel flow and nodal power distributions are used to calculste g thermal equilibrium quality at each node in each channel. Quality is a thermodynamic property of a liquid vapor mixture defined as:
! b _- h he _
b_h- (2.45) hs -h 4 h I !l I where: h = enthalpy of a boiling or subcooled mixture, BTU /lb. hg = enthalpy of saturated fluid, BTU /lb. 18 r I
I ! I hg= enthalpy of saturated vapor, BTU /lb. h fg
= enthalpy of vaporization, BTU /lb.
Prior to boiling, h is less than hf and X is negative. Quality is calculated internally for each node k in each assembly using a heat balance beginning at the assembly inlet and ending at the mid plane of the node: (~A:~St-D
~
o i] g g'd (2.46) 4g . 3 A=\ - I where: I gh o= core inlet subcooling. OA o =h f
-h inlet
- A radial distribution may be imposed ond h ,o I W f3 = Assembly in-channel flow (M1b/hr), not including leakage flow.
P ijk = Nodal relative power distribution.
- 3) Nodal void fraction (R ) is calculated from the EPRI void quality correlationdescribed$elow. In-channel relative water density is then calculated as:
U ijk gg/gf) (2*47)
= 1.0 - (Rg + Rg ')(1 R' is an additional change in void fraction to account for any voiding ing the bypass region. The relative importance of bypass voiding in determining node k is itself a function of in-channel voiding:
R'g = BV[C' + C" R] g I I 19 I
I H where: BV is the bypass void fraction. is the fluid density in Ib/ft calculated 3 internally from steam ble function? at reactor pressure PR. is the vapor density. The factor (1-A;/8f) causes the vapor in p$ebubblestobeincludedinU t ijk*
- 4) The array lif is available to be used in cross section input fits.
It is also u d in updating the void history array Vijk* 2.3.1 Void-quality Relationship l The relationship between local equilibrium quality and local void I is given by the so-called "EPRI" void relationship developed by Zolotar and Le11ouche (10). This relationship accounts explicitly for subcooled boiling and its dependence on heat flux. It is a drift flux relationship of the form: I ol. =
< X '>
Co.%x> + gjbO-<xs + Ps Voi (2.48) where: <X> is the flow quality; Co is the concentration parameter; l V is the drift velocity of the vapor relative gj to the liquid; i 1 G is the mass flux; gg,g i are the mass densities of liquid and vapor. The EPRI void model includes equations which specify the flow quality <X> I and C, in terms of the thermal hydraulic variables. Justification for the EPRI void model, including comparisons with measured data, is given in References 10 and 11. I 20 I
I I 2.3.2 Leakage Flow and Bypass Voiding In a BWR a portion of the total core flow does not flow up the channel but instead flows up the inter-channel gap around the control blades , and instrumentation tubes. This leakage flow, WL, is input as a function of core flow. The bypass may boil in some systems and an optional voidfractioncorrelation(gwithbuilt-inconstantsisavailable. The effect of voiding in the bypass region may be included in the relative water density. These are used to account for the relatively high importance of I the bypass water in the calculation of node k.at high in-channel void fractions. In SIMULATE for a BWR U k is defined to be in-channel relative water density: it does not ordinari address the out of channel water. 2.3.3 Core Inlet Subcooling and Heat Balance The input value of core inlet subcooling may be overridden by an I internal BWR heat balance calculation. Its use is desirable because the inlet subcooling is a function of both power and flow, which may be varied independently in a BWR. Most parame.ters needed are supplied as constants I and fits where appropriate. No case dependent input is required. To derive the equations needed, the BWR reactor system is divided into four control volumes as shown in Figure 2.2. The terms have the following definitions: Flows, all Mlb/hr W Total core flow T W3 Steam flow from vessel W 33 Flow to downcomer from steam separators I W pg W CR Feedwater flow Control rod drive leakage flow Enthalpies, all BTU /lb hg Core inlet h Core outlet o h 3 Exit steam from vessel h 33 Separators flow to downcomer h pg Feedwater inlet h yp Exit of jet pumps l h CR Control rod drive leakage h Saturated liquid f hg Saturated vapor h fg Enthalpy of vaporization hg Core inlet subcooling l Heat Sources and Losses, all MBTU/hr Fission power 9 fission Recirculation pumping power delivered to flow QRP Clean up system heat removal QCU L ss from system Ql oss 21
w I I Moisture and Carry Under Fractions Fg The moisture fraction (decimal) in the exit ' steam F CU The vapor fraction in the recirculating flow from the separators. Mass and energy balances for each control volune yield core inlet enthalpy: I ~W Fw *cR)bn+ h brw + N hen ~ Geu~ hig[b] b.~
^
y T (2.49) Many of the intermediate terms are printed in a detailed output report. Enthalpies are derived internally from ste.am table functions. 2.3.4 Pressure Drop The pressure drop calculation includes explicit consideration of the pressure changes across four distinct regions: o Inlet orifice; o Subcooled portion of the active core; o Bulk boiling portion of the active core; o Channel exit region at the top of the core. Included in the calculations are the effects of acceleration, I friction, gravity and local losses as shown in Equation 2-2 on page 7 of the report on our " Steady-State Core Flow Distribution Code".(II). Equations 2-3 through 2-9 of Reference 11 are also used in SIMULATE to calculate these I individual components of the pressure drop. For use in SIMULATE, however, the single phase friction factor, two phase multiplier, and form loss coefficient appearing in these equations are parameterized as fits to local I values of flow, pressure, etc. Reference 11 (Table 5-8) shows the good agreement obtained between FIBWR calculated and measured core pressure drops. 2.4 The Coupled Nuclear-Hydraulic Iterations The coupled nuclear-hydraulic iterations are performed to compute the core power distribution while using cross sections which are consistent I with the power distribution and the core's history. The solution process is divided into the iteration levels shown 22 I
I in the flow chart Figure 2.3. This is an expanded view of the program segment NUCLER in Figure 2.1. The calculation flow is summarized below. The iteration is begun with an estimate of the source and power distributions; this may come from a previous case or a flat guess may be selected. Water density is calculated from void fraction usirg the built-in "EPRI" void quality correlation. In the flow balancing iteration, flows I are adjusted so that the pressure drap in each channel is equal to the core average pressure drop. The BWR heat balance may be used to automatically compute the core inlet subcooling for given power and flow conditions and during criticality searches. Nodal cross sections are then calculated from the input fits using the latest local estimates of nodal power and water density and the local I history data on nodal exposure, void history, fission product concentration, etc. The one group parameters k,,, M2 and Q re calculated and provided to the internodal neutron transport calculation. I The core power distribution is computed from the resulting source distribution using the available cross section data. The thermal leakage correction is generated and applied to the thermal flux if requested. I Processing then continues as shown in Figure 2.3. The boron search and the Haling iteration are performed at the void iteration level, while control rods, power or flow are adjusted only in the control level af ter both source I and void levels are converged. The two innermost iteration levels are the inner and outer source I iterations used to solve the neutron balance equation for a given set of Cross sections. I In matrix form, the equation to be solved is: Mb*N
-- GFF (2.50)
I where both M and F have seven non-zero stripes. M represents the diffusion and absorption terms, F the fission terms. Equation (2.50) has the same form as does the one-group finite-differenced diffusion equation for three I dimensional rectangular geometry, with the exception that the source term on the right side couples six adjacent nodes to the node of interest. The matrix M_ is irreducible.(13) For all practical situations, it is also diagonally doc!4tr.rg 1.e., g l % >, [ lM;fl h ali j If the unknowns are order ow by row and plane, M_ is also a consistently ordered two-cycle matrix. These properties give assurance that the 23 I
I block successive over-relaxation method with an optimum overrelaxation f actor will converge when applied to solving an inhomogeneous matrix equation where I M is the matrix of coefficients. Given the properties of M, the two-level iterative scheme which I has been applied to the multi-dimensional of computer codes such as PDQ-5 and PDQ-7. f on equation in a number is applicable. The outer iterations can be written as
~ (2.51)
I m-grF (2.32) S ( n+1)=
$ (M+1)
I # (2.s3) KN (n +d = Kgg(F p g Ah) (n ) i} Jl F S "*' l} I E ations may be accelerated I Af t r several outer iterations, thgi through the w of Chebyshev polynomials.I ' The two source distributions fron the two previous outer iterations are used with the present source distribution to provide a new source distribution through I extrapolation. The inner iterations are required to iteratively invert the matrix M in Equation (2.51). The line successive displacement technique is used to carry out this inversion. The source iteration routines include internal symmetry boundary conditions. i I I I I 24 I
m m m M M M M M M M M M M M M M M M M 3 Begin SIMUIATE Run
\/
Read Dimension and File Cards N /\ /\ s
/ 'N
%/ \/ \/
INPUT NUCLER ANALYS Input Processing Coupled Nuclear- Detector Response Hydraulic Iterations Calculation l V End SIMULATE Run FIGURE 2.1 Overall Flow Chart of the SIMULATE Program
I I Downcomer and I Recirculation System W h3 g-m
.r________ FSteamSeparators_ _ _ _ r_I _____ exit Il Heat Loss i Steam QLOSS 2,
;II l I l '
l l SS uI' l I Il I Feedwater Flow I
- L - -- - n----- J wpg' hm l m [ II- -Core-~~~ ---- 1
, - W,h I I g I
l ll II T o i I i i 11 1 l - ll I cleanup system g r gg Q heat removal r FISSION t QCU w I - I 0 ) y l i i Pep 1 Ig I Recirculation Pumping I f, a 1l I I Power QRP g l t___ 7 ll ll _.it_ _ _ _ _ JL _____J l l I , l W k JP, h JP ____---q N'hi T i I l I l I Lower l l Plenum n g L__________ ------- J l
~ NCR, hCR l
Control Rod Leakage l
- Figure 2.2 Control Volumes and Flows for the BWR Heat Balance.
26 ,I
I I Enter I Enter iterations after case input is completed l An initial power distribution is provided gp 3 E 1, Calculate the control flag array U ijk 1 Calculate the moderator density U lik p________q _________, Generate k= and I a I E, k., I i I cross sections. Update exposure in Haling iterations. Solve the neutren talance equation with I s i s S igy l I 8 inner and outer source iterations e outer 8 source ', l Compute the power distribution and the l thermal leakage correction. i Pi jk,Tijk i t_____--_,._________ l Boron Search Adjust boron for criticality (option) ! void Test for convergence of the void level iteration Adjust power, flow or control rods for Searches , criticality (options) control Test for convergence of control level iteration (if in use) Update exposure and nuclide concentra-Ei jk, N n ti ns in depletion cases, l l Test for final c.imestep lW exposure
/
1E 1F Return to INPUT or ANALYS as shown Continue in Figure 2.1 FIGURE 2.3 Coupled Nuclear-Hydraulic Iterations 27
TABLE 2.1 Independent Variables Available to Cross section Input Vectors Variable Comments Ei jk Nodal Exposure, CWD/T Control Flag, f CTi jk = 1 for uncontrolled
= -1 for controlled P*ijk Node power relative to core average rated value .
U ijk Relative Water Density Void History Vi jk square root of fuel temperature, K
~
[T fijy CB Boron number density related variable CB Uijk Boron concentration related variable h Axial position in cm from bottom surface of core. CF ijk Control history I I g Nuclide egentrations, atoms /bn-cm Iodine, I g Ny N,y Xenon, Xe l35 N, p Promethium, Pm 149 ite N sm s _ari_ , sm g . I I g u I .
I ,
)
TABLE 2.2 Cross Sections and Basic Equations for the Two Group Input Method I I Macroscopic Cross Sections Microscopic Cross Sections 1 E I U trl trl 2 I,g 2 0,g 3 E 3 U rl rl 4 ME g7 4 M0 f1 5 KE 5 Ko gg gi 6 E tr2 tr2 7 E a2 a2 8 VE 8 vo f2 f2 9 KE 9 g2 KOf2 I j Basic Equations Used: ,,
"E f1 + " f2 I
r1 i E E r1 a2 Eal + TEr1 i T is the optional thermal leakage correction. l 2 2 1 I i M "T+L E ! " 3Etrl(Eal + Er1) + 3E tr2 a2 Input 0,1 and a2 c f r the fission products. l lI l i 'I 2e I
I I 3 BASES FOR CONFIDE'NCE I , 3.1 Summary I Comparisons with higher order calculations help to establish confidence in the methods described here. The ultimate test, however, is comparison with actual data measured in operating plants. Because our primary concern is the Vermont Yankee plant, we show comparisons of I eigenvalue and TIP traces over all seven past cycles. These cover a wide variety of fuel designs and core conditions, with some batches in the later cycles achieving the design discharge exposures. The Quad Cities Unit 1 I core has also been included because it was gamma-scanned after Cycle 2, thus providing an independent verification of power distribution. These comparisons with actual data from operating plants constitute an integral I verification of the whole calculational technique -- lattice physics, neutron transport in the core, void quality relationship, and 3-D feedback. They are buttressed by comparison of SIMULATE with higher order I calculated results. These additional comparisons do not include fee.dback -- they are performed with an input spatial distribution of cross sections. However, they verify certain aspects of the model in more detail. Two-I dimensional, few assembly comparisons between SIMULATE and 4 group, heterogeneous PDQ's (each fuel pin unit cell represented separately) show the adequacy of the internodal transport model and the assembly homogenization. This is further verified by quarter core PDQ-SIMULATE I comparisons (again with explicit fuel rod unit cells). Thus the steady state methods have been checked against both a large I number of actual operating data and against higher order calculations. Both indicate the adequacy of the methods described here. For Vermont Yankee, the comparisons indicate standard deviations .E lW of: 0.0027 in hot efdenvalue; 'I O.003 in cold eigenvalue; 6.4% in power distribution. 3.2 Description of the Cores Modeled Table 3.1 lists the important characteristics of the Vermont Yankee reactors on which the methods presented here have been I and Quad Cities tested. Table 3.1 summarizes the operating history of Vermont Yankee fuel for Cycles 1-7. Quad Cities operating history is given in Reference 16. Figures 3.1 and 3.2 show the core layouts for the two plants. Esth plants are typical GE designed BWR's and use typical CE ft;el and control rods. The power, flow, water density, control rod insertion and inlet subcooling for the seven Vermont cycles are plotted against core total (integrated) exposure in Figures 3.3 to 3.7. The total (integrated) exposure 30 I
I I is the total energy generated by the plant up to any statepoint, divided by the core mass. It is used here only because it is an exposure variable I which provides a unique, one-to-one correspondence with statepoint. (The actual core average exposure is decremented by exposure discharge at the end of each cycle and therefore assigns the sar.3 exposure to several I statepoints. Compare Figures 3 8 and 3.9). A significant number of off-nominal conditions (i.e., - not full power, full flow) are included. Figures 3.59 to 3.63 show similar data for Cycles 1 and 2 of the Quad Cities 1 plant. 3.3 Features of the S*MULATE Core Models 3.3.1 Ccometry Models I Depletion calculations for all cores are usually carried out in a quarter core geometry, unless the control rod patterns or core loading I are not quarter core symmetric. For Vermont Yankee and Quad Cities, depletion was calculated with a quartar core model with reflecting (zero current) conditions along the quarter core boundary. One node per assembly was used horizontally and twenty-four nodes axially. The resulting nodes are six-inch cubes. I Shutdown margin calculations utilized the minimum symmetry needed to represent the stuck control rod quarter core for the central rod, half core for the rods on the line of symmetry, and full core in other cases. 3.3.2 Neutronics Models In all cases, fundamental physics parameters for fuel nodes were I obtained by use of the CASMO program. The CASMO models had the following features: I - The standard twenty five group library was used, with twelve macro groups for the cylindrical calculation and seven groups for the two-dimensional calculation. Copletion calculations were performed unrodded at 0, 40 and 70 percent void. Periodically during the depletion, branch calculations were made at off-nominal values of void and fuel temperature, and with control rod inserted. Additional branches to cold conditions were also performed using the history from the hot depletions. The branches are performed at eight exposures between 0 and 30 GWD/T.
- For use in S1MULATE, the resulting sets of 9 macroscopic, two-group cross sections were characterized in a library of tabular I and polynomial fits, as a function of the independent variables shown in Table 2.1. A separate hot and cold library results for each fuel type.
The core depletion calculations were performed using the actual control rod patterns logged by the process computer at the time the TIP sets were taken. The burnup increment for each depletion interval was 31 I
I I determined f rom the plant log of average daily power. The TIP sets used were selected to give burnup increments of no more than 500 MWD /T and to I represent equilibrium xenon conditions, so that the option for equilibriu-xenon could be used during depletion. Typically this yields 10 to 20 steps during each cycle. The conditions at each state point may be seen in Figures 3.3 to 3.7 for Vermont and 3.59 to 3.63 for Quad Cities. Albedo's for the Vermont Yankee model were initially obtained f rom I first principles calculations, and were then adjusted slightly to give good agreement with the quarter core PDQ calculations discussed in Section 3.6. The same set of albedo's was used on all cycles. For Quad Cities, the albedo's used were identical to the VY values for each type of fuel I reflector interface. (The interface type refers to the number of external f aces and to whether adjacent assemblies yield re-entrant corner configurations.) 3.3.3 Thermal-llydraulics Models The square root of fuel temperature was represented as linear in I nodal power. The internal flow balancing iteration was used to adjust active channel flows during the calculation to equalize core pressure drops across all assemblies. I The bypass void correlations were used during the portion of Vermont Yankee Cycle 3 when the bypass flow holes in the bottom plate were plugged. At this time, fuel with holes drilled through the bottom fittings to enhance The correlation was also employed in I the bypass flow was not yet in use. later cycles when a significant amount of undrilled fuel was in the core. The inlet subcooling was determined from the internal heat balance I using a tabular representation of feedwater temperature, leakage flow, etc. The tables were obtained from the observed values at the Vermont Yankee plant. 3.4 Comparisons With Data Measured at Vermont Yankee Cycles 1-7 3.4.1 Ilot Eigenvalues Figures 3.8 and 3.9 show the eigenvalues obtained froe SIMULATE calculations of Cycles 1-7, using the observed critical control rod I positions. Consistency of results is excellent, both within any one cycle and from cycle to cycle. The consistency is especially impressive considering the range of fuel types (7x7 and 8x8), fuel enrichments (2.2 to 2.9 w/o), burnable poison (boron stainless curtains and gadolinia), power I level (50 to 100%), fuel bundle exposures (0 to 25 GUD/T), control rod insertions (ARO to 950 notches), and core flow (70 to 100% of rated). The average eigenvalue for all seven cycles is 1.0019 with a standard deviation of 0.0027. When results are referenced to the everage for each individual cycle, the total standard deviation is only 0.0012, 32 I
I I 3.4.2 Flux and Burnup Distributions in the Core The adequacy of in-core power distributions has been checked in two ways: Comparison of measured and calculated TIP readings;
- Comparison of end-of-cycle assembly burnup distributions from the process computer and from calculation.
Figures 3.10 to 3.30 show the core average TIP readings near the beginning, middle and end of each of the seven Vermont cycles. Comparisons for individual TIP strings are shown in Figures 3.31 to 3.51. Interpret these figures as follows: every page contains a number of subplots, each being a comparison for an individual TIP string whose I plant coordinate number is shown at the top of the subplot. The arrangement of subplots on the page is roughly the arrangement of TIP strings when one looks down on the core from above. The top of the core is at the top of I each subplot. Measured TIP data are shown as X's, calculated as the continuous line. Tic marks on each horizontal axis are at TIP readings of .5,1.0,1.5, 2.0, and 2.5 relative to a core average value of 1.0. I Each subplot may contain up to two vertical markers with horizontal caps; these show the insertion depth of the two control rods which lie at the diagonally opposite corners of the four-assembly array surrounding the TIP string. The subplot in the lower right-hand corner contains the averages I and is identical to the full page plots previously discussed. The measured and calculated core peak to average value of TIP readings (the ratio of max value anywhere in the core-to-core average value for the TIP set) have been evaluated statistically. The overall RMS difference for all statepoints is 6.4%, which is acceptably small. Part of even this difference is probably an artifact arising from I "TIP asymmetry" -- differences between the readings of symmetrically located TIP's, due primarily to bowing of the TIP tubes. Figures 3.52 to 3.58 show the calculated and measured assembly burnups at the end of each of the seven cycles calculated for Vermont Yankee. The good agreement is evident. 3.4.3 Cold criticals !g The capability to calculate shutdown margins for Vermont Yankee 3 has been assessed by comparison of calculated and measured eigenvalues for cold critical conditions. Table 3.3 lists the conditions at which the measurements were made and the resulting eigenvalues. The average eigenvalue is 0.989, with a standard deviation of 0.003. We conclude that a cold eigenvalue of 0.989 should be used as critical in assessing shutdown margins. I 33 I
I I 3.5 Comparisons With Data Measured at Ouad Cities Cycles 1-2 3.5.1 Hot Eigenvalues Figure 3.64 shows the eigenvalues obtained from SIMULATE calculations of Cycles 1-2, using the observed critical control rod positions. I Consistency of results is excellent, both within the cycles, from cycle-to-cycle, and with the Vermont results. The average eigenvalue for the two cycles is 0.9976 with a standard deviation of 0.0027. 3.5.2 Flux and Burnup Distributions in the Core The adequacy of in-core power distributions has been checked in I two ways: Comparison of measured and calculated TIP readings; Comparison of measured and calculated gamma scan data. I Figures 3.65 to 3.70 show the core average TIP readings at the beginning, middle, and end of each of the two Quad Cities cycles. Comparisons for individual TIP strings are shown in Figures 3.71 to 3.76. These should be interpreted as explained in Section 3.4.2. The gamma scans made by EPRI(17) provide an independent check on the power distributions. A radial comparison (i.e., assembly total) is shown in Figure 3.77 and an average axial comparison in Figure 3.78. 3.6 Comparisons With Higher Order Calculations The comparisons shown here are of two kinds:
- Two-dimensional (X-Y), few bundle comparisons between SIMULATE I and four group, heterogeneous PDQ's with each unit cell and control rcd represented explicitly in the PDQ. These verify that the bundle-average constarits from CASMO, together with the SIMULATE nodal neutronics yield adequate nodal flux and = power distributions.
Two-dimensional (X-Y) quarter core comparisons between SIMULATE I and four group, heterogeneous PDQ's with each unit cell and control rod represented explicitly. These comparisons between SIMULATE and PDQ were performed to verify the adequacy of the SIMULATE calculation of internodal neutron transport. For this purpose, feedback was omitted and a set of void and exposure I distributions was specifically chosen to accentuate mismatches between assemblies. The SIMULATE calculations were performed exactly like the analyses of operating cores (except that feedback was omitted and the g problems are only two-dimensional). The PDQ calculations were heterogeneous g analyses with macroscopic cross sections for the various unit pin cells and unfueled regions taken from CASMO results. Unit assembly PDQ
- calculations, with the same mesh spacing as in the few-assembly calculation,
= 34 I
I I were used to adjust the diffusion theory cross sections for the control rods and for gadolinia unit cells so that they held down the same reactivity as they did in the unit assembly CASMO. The same " empirical blackness I theory" technique was used in analyzing the strong absorber criticals discussed in Section 2.1.3 of our lattice physics report (19). 3.6.1 Few Assembly PDQ Calculations Figures 3.79 to 3.81 compare power distributions and eigenvalues I from a nine-assembly array as calculated by SIMULATE and by four-group, heterogeneous PDQ's. The outer eight assemblies of this set are always at 40% void, 25 GWD/T exposure. The central assembly is varied from 0 to 70% void, and from 5 to 30 GWD/T. Even with these large mismatches, there I is less than 2% difference between the bundle powers from the detailed PDQ and the coarse mesh SIMULATE. The eigenvalues match within 0.06%. 3.6.2 Quarter Ccre PDQ Calculations Figures 3.82 to 3.84 compare power distributions and eigenvalues f rom two-dicensional quarter cores as calculated by SIMULATE and by two I group, heterogeneous PDQ's, with each fuel pin unit cell and each control rod represented explicitly. The three cases are typical of radial planes through the bottom, middle and top of an operating Vermont Yankee core, I but do not exactly represent any specific core. The PDQ's and SIMULATE's were run for exactly the same bundle average conditions. Bundle powers agree to within a couple of percent, except for a few of the very low power bundles. Eigenvalues agree to within 0.11%. I I I I I I I as g I
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@ IM LOCATION I a su LOCATION
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' - @ LPRM LOCATIO.e (LETTER INDICATES TIP MACHINE)
I S LPRM LOCATION ICOMMON LOCATIO'e POR ALLTIP MACHINE 58 l S tRM Locations I O SRM LOCAftOMS ! $ SOURCE LOCATIO*ss
- E E FIGURE 3.2 Layout of the Quad Cities Unit One Core
- 37
W m e m m W W W W m m W W W W m W W FIGURE 3 3
- VERMONT YANKEE CYCLES 1 THROUGH 7 o 7X7-WITH CURTAINS. 8X8 RNO 8X8R FUEL TYPES
. o.
. PERCENT OF CORE. POWER I,
o o o- s1A s-.n u h 8- { x 4 g E8- N I .i u 84
? a LEGEND s-
$8 i CYCLE 1 uS_
$* 9 CYCLE 2 a- a CYCLE 3 2 CYCLE 3R S a CYCLE 4 :
o. n CYCLE 5
" a CYCLE 6.6R
, CYCLE 7 o
'0 '. 0 0 5'.00 l'O .00 l'5.00 2'0.00 2'S.00 3'O.00 3'S.00 4'O.00 4'S.00 S'0 00 REACTOR TOTAL EXPOSURE. GWO/T
M M o c. b s M A 6 A , o 12334567 c. M h EEEEEEEE 4 D LLLLLLLL N CCCCCCCC E YYYYYYYY M G CCCCCCCC o S E c. E L i 9 ' 9 4 n a 7 b 4 P Y M T L o E c. M 7F HR U
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~ U'uzd 5$2 wD $'de woe'E$E M g E
FIGURE 3 6 VERMONT YANKEE CYCLES 1 THROUGH 7 7X7 WITH CURTRINS, 8X8 RNO 8X8R FUEL TYPES o 9
?,. CONTROL ROD NOTCHES INSERTED 8 "ob-7 8
ah-U x
$8 3d.*
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h5- i g LEGEND E8 ad. i CYCLE 1 o' + 9 CYCLE 2 z
' CYCLE 3
' CYCLE 3R A
8 Wk , a CYCLE 4
- d. CYCLE 5
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" 7 YCLE 7 8 ,
%.00 5'.00 l'O . 00 l'5.00 2'O.00 2'5.00 3'O.00 3'5.00 4'0.00 4'5.00 5'0.00 RERCTOR TOTAL EXPOSURE, GWD/T
_j
FIGURE 3 7 I VERMONT YANKEE CYCLES 1 THROUGH 7 7X7 WITH CURTAINS, 8X8 AND 8X8R FUEL TYPES 8 ~
- f. CALCULRTED INLET SUBC00 LING 8
8-W OE 38' 8 58 e ";;- O w c._
/) *
$ ( LEGEND
$8 N 3"* i CYCLE 1 m 9 CYCLE 2 u , CYCLE 3 9 CYCLE 3R 8 4 CYCLE 4 m.
~ _n CYCLE 5 n CYCLE 6,6A 7 CYCLE 7 8
b.oo s'.00 t'o . 00 t's .oo 2'o.00 2's.co 3'o.00 3's.co 4'o.00 4's.00 s'0.00 REACTOR TOTRL EXPOSURE, GWO/T
e 0 0 O m '5 R 6 0 R . 0 12334567 5 4 EEEEEEEE D LLLLLLLL N CCCCCCCC YYYYYYYY G CCCCCCCC 0 0 S E L i 9 1 1 4 s a 7 '0 E WE 4 P Y T 0 L 0 E 5 U 3T 7F / W HR G8 UX O8 R HO E M 0G 0 0
'3 E D
W R TN V U I R S T i 8 C 0O 8 P SX E 0. X 3 E8 F '5 E WRE U G L C , YS E F K 2 L A I CN 0 T O MF ER ET KR I D E T A
'0
- 0. T 2
R NU O AC L T Y U C H C 0 A TT L 0. E A 5R NI OW C 1 M R7 EX V7 0 0 Q 'O l 0 f 0
'5 E 0 0
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M M ' M M M. M M M M . M FIGURE 3 9 VERMONT YANKEE CYCLES 1 THROUGH 7 7X7 WITH CURTRINS. 8X8 RND 8X8R FUEL TYPES CALCULRTED K-EFFECTIVE
}.
S 4 E 2 w Z C5 w-ii W v. c LEGEND i CYCLE 1
$ 9 CYCLE 2 do~ a CYCLE 3 u 9 CYCLE 3R
__L_ CYCLE 4
, n LYCLE 5
<= a CYCLE 6.6R o- , CYCLE 7 E. '
t'4 00 t's .co l's .co z'o.co e'.co s'.co io.no t'2 00
%.00 2'.00 4'.00 CORE RVERAGE EXPOSURE, GWD/T
W M M FIGURE 3.10 CORE AVERAGE AYIAL TIP TRACES 81/02/06. VERMONT CYCLE 1, TIP CALIBRATION 3. SEPT. 22, 1972. 817 mkt, 48.2 MLB/HR S S-g -x- = MEASURED N' - = CALCULATED 8 b-8 6; 5-t 0 i i-8
$~
l O
/>-
l i S* l 3 .00 C'.2J O'.50 0'. 7 b 1'.00 l'.25 1'.50 l'.75 0'.00 2'.25 2'.50 BOTTOM OF CORE CORT EXPOSURE % PCWER % FLOW K-EFFECTIVE 120 51 3 100.4 1 01015
E $
- OI .N s N N G*
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m bM M M M M M M M M M M M M M M M M FIGURE 3 12 CORE AVERAGE 9XIAL TIP TRACES 81/02/06 VERMONT CYrLE 19. TIP CALIBRATION 24. SEPT. 17. 1973. 1087 MWT. 42.5 HLB 8 e* 8 -x = MEASURED E.
** = CALCULATED
~
d-t 8* t 8 d-8 I s-O I 3 .00 0'.25 0'.50 0'.75 l'.00 l'.25 l'.50 l'.75 2'.00 2'.25 2'.50 BOTTON OF CORE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE 3 368 68 2 88.6 1.00516
M M M M M M M M M M M M M M FIGURE 3 13 CORE AVER 4GL fiK!AL TiP TR4CES 461/02/06 VERMONT C(ClE 2, TIP COLIBqqiIGN 35. F Ets . 15. 1974 1516 MWT. 46.5 MLB/H 3 ([ 8 -x- = MEASURED
". = CALCULATED 3
6.- 8 s~ oo r 3
?-
S a-S A- . l 0 ' % .00 0'.25 0'.50 0' 75 l' 00 t '. 2 5 1'.50 t '. 7 5 [.00 2'.25 2'.50 l B0TTON Of CORE i CORE EXPOSURE % POWER % FLOW 6-Ef f ECTIVE 4 309 95.2 96 8 1 00404
FIGURE 3 14 CORE RVERRGE RXIRL TIP TRRCES 81/02/06. VERMONT CYCLE 2. TIP CALIBRRTION 41. APR. 25. 1974. 1258 MWT. 45.6 NLB/H S
~
-x- = MEASURED g
E - = CALCULATED E b" 8
, 5-
- r
)
3-E
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r S 8 - > T.00 .,p'. 2 6 0'.50 0'.75 l'.00 l'.25 t'. 50 l'.75 2'.00 2'.25 2'.50 BOTTOM 0F CORE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE 5 269 79 0 94 9 1 00598
~ __ _- _ _ _ _ _ _ _ _ _ _ - . - _ _ _ _
M M M M M M M M M M M M M FIGURE 3 15 CORE RVERAGE RXIRL TIP TRACES El/02/06. VERMONT CYCLE 2 T IP C AL IBRAT ION 48. ' SEPT 5. 1974. 1257 MWT. A6 6 MLB/HR S'
?r E -x- = MEASURED
" = CALCULATED S
8 <
)
3 8 x S i
- 8. . -
J 4 O N , 8
% .00 G'. 2 5 0' . ',0 C' 7 5 l'. D C l'.25 1'.50 1'.15 '[.00 2'25 [.50 BOTTON Of CORE CORE EXPOSURE '/. POWER % FLOW K-EFFECTIVE 7.!!7 78.9 97.0 1.00699
FIGURE ~3 16 CORE AVERAGE AXIAL TIP TRACES 4 1/02/09 VERMONT CYCLE 3 LPRM CALIBRATION 61 01/08/75 CTP:1588 WT=46.1 5
-j.
o -x- = MEASURED 9
;;- - - CALCULATED S
6 8 ' , y 5' r S 8 g- . I S 4- , 8
%.00 o'.so o'. 7 s i.co i.:s t '. s o s '. 7 s 2'.00 2'.25 2'.50
.* O'. :s BOTTOM OF CORE CORE EXPOSURE */. POWER */. FLOW K-EFFECTIVE
.753 99.7 96 0 1 00213
FIGURE 3.17 CORE AVERAGE AXIAL TIP TRACES 11/02/10
. VERMONT CYCLE 3 LPRM CALIBRATION 119 10/29/75 CTP:1581 WT.48 S
S-
-x- = MEASURED 8
E
" - = CALCULATED E
A 4.
~
v. N r t 2" + , t 8=- 1 S 1 E~ 8 T.00 .,p'. 2 5 0'.50 0'.75 1'.00 l'.25 l'.50 l'.75 2'.00 2'.25 2'.50 80TTOM OF CORE CORE EXPOSURE */ POWER */. FLOW K-EFFECTIVE 5 637 99 2 100.0 99903
FIGURE 3.18 ,_ CORE RVERAGE RXIRL TIP TRRCES 81/02/10. VERMONT CYCLE 3 LPRM CALIBRATION 176 06/05/76 CTP=1455 WT=47.7 8 . 5-
-x- = MEASURED o
9 E- --- = CALCULATED 2 3 , d-8 E. W r S E. O E-S E-8 k .00 0'.25 0'.50 0'.75 1'.00 1'.25 t '. 5 0 l'.75 2'.00 2'.25 2'.50 00TTON OF CORE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE 9 666 91 3 99 5 1 00133
m' W W W . M M M M M M M M M M M M l FIGURE 3 19 CORE AVERAGE AXIAL TIP TRACES 81/02/11 VERMONT CYCLE 4 L PRM CALIBRATION 188 08/19/76 CTP 1517 WT=48 l S
- h-he
-x- = MEASURED g
c7 - = CALCULATED S b-t g n g 5-r S 5-8 - e 5 . g,- O 9 . o'.so l'.co l'. :s t'. so i.75 2'.00 2'.25 2'.50 (b .co .' p' 2s
. o'. 7 s BOTTON OF CORE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE 5 843 95.2 99.9 .99822
. 0 1 5 1 . '2
/
2 0
/
1 D 6 E 4 D E T A 2
'2 R L 8 U L S C E _
A L V _ 0 E A I 8 _ 4 M C 0 _
= 0 T 2 T = = C0 W -
'2 E0 x F0 6 - - F E1 1
5 5 K 1 7
= '1 SP ET W0 CC O A L5 R7 0 F8 T7 5
/ %
P8 'l E I 1 R T/ O 1 C R L0 5 E1 0 A 2 I 0 2.OF W . 3 X3 'l O 5 R2 M P9 E R O %
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'0 E
L C Y C 6 2 T '0 N O M R E 0 V 0 Eg 0 N" Si 85 S5 8g 3; E% r g l fl llll I
i l FIGURE 3 21 CORE AVERAGE RXIRL TIP TRACES 81/02/11. VERMONT CYCLE 4 LPRM CALIBRATION 259 05/25/77 CTP=1584 WT=47.9 E b 1
-x- = MEASURED h- - = CALCULATED 3
9. 8 " L
- {
u,
@ M S
5- 3 r-W , S - g,- . O.
% .00 0'.25 0'.50 0'.75 1'.00 1'.25 l'.50 l'.75 2'.00 2'.25 2'.50 BOTTOM OF CORE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE 11 313 99.4 99 7 1 00098
-M- M M M M M M M M' M M M M M M M M M M FIGURE 3 22 CORE RVERAGE RXIRL TIP TRRCES 11/02/12 VERMONT CYCLE 5 LPRM CALIBRATION 282 10/28/77 CTP21586 WT=46.7 3 e-g -x- = MEASURED C' = CALCULATED S ' f. 8
. 5-x 8
y. 8 s-
- 8. .
8
%.00 .,,0'. 2 5 0'.50 0'.75 l'.00 l'.25 t '. 50 l'.75 2'.00 2'.25 2'.50 60TTOM OF CORE CORE EXPOSURE % POWER '/. FLOW K-EFFECTIVE 8 165 97.1 97 3 1 00205
FIGURE 3.23 CORE RVERAGE RXIRL TIP TRACES 8t/02/12. VERMONT CYCLE 5,.LPRM CALIBRATION 320 04/05/78 CTP=1586 WT=46.5 S N k. l ' -x- = MEASURED g c7 --- = CALCULATED
? e C- ,
8, 5
$ x 8
5-8 s-S k 8 l'.co t'. so t'. 7 5 2'.00 2'.25 2'.50 k.oo o'.:s o'.so o'. 7s t '. :s BOTTOM OF CORE CORE EXPOSURE */. P O W ER */. FLOW K-EFFECTIVE 11.263 99 6 96 9 .99974
FIGURE 3 24 CORE AVERAGE RXIAL.TIP TRACES ~81/02/12. VERMONT CYCLE 5 LPRM CALIBRATION 352 08/25/78 CTP 1550 WT=d7.9 3 d,- i n -x- - MEASURED 9 i(' - = CALCULATED E d-P g . n , g 1-r 1 3- x k E
- g. v
.c M .
$~
E Q (; - k.00 , 0'. 2 5 0'.50 0'.75 l'.00 l'.25 l'.50 l'.75 2'.00 2'.25 2'.50 60TTOM OF CORE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE 13 265 97.3 99.8 1 00272
W W m m M M - M M M M M M M M M M M M M FIGUllE 3 25 CORE RVERAGE RXIRL TIP TRRCES 8t/02/13. - VERMONT CYCLE 6 LPRM CALIBRATION 371 11/14/78 CTP=1588 WT=46 5
.3
- g -x- = MEASURED
~ E~ - = CALCULATED i
f. 8 4.
~
cn O W ' E d. 8 5~ l k i E a- . 8
% .00 0'.25 0'.50 0'.75 1'.00 l'.25 l'.50 1'.75 2'.00 2'.25 2'.50 BOTTON OF CORE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE 9 249 99 7 96.9 1 00098
m m M M M M M M M m m m m FIGURE 3 26 CORE RVERAGE RXIRL TIP TRRCES 11/02/13 . VERMONT CYCLE 6 LPRM CALIBRATION 392 03/14/79 CTP=1424 WT=37 3 i E 5-i
-x- = MEASUPID g
E" - = CALCULATED ! E C' c 8
, 5- t 3c 2-l l ; 8 s- .
E g- i 8
.00 . A'.25 0'.50 0'.75 l'.00 l'.25 l'.50 1'.75 2'.00 2'.25 2'.50 BOTTOM OF CORE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE 11 739 89.4 77 7 1 00074
m m M M M M M M m m m W m M m m m j FIGURE 3 27 CORE AVERAGE RXIRL TIP TRACES 81/02/13. VERMONT CYCLE 6R LPRM CALIBRATION 435 09/20/79 CTP=1397 WT=47.7 S 8 -x- = MEASURED
= CALCUIATED 3
- d-t 8 a
*. 2 10 x:
F i l d.
~
n ! 8 g. 4 5 . 8
%.00 g'.26 o'.so o'.7s l'.co l'.25 t'.so l'.75 2'.00 2'.25 2'.50 BOTTOM OF CORE i
CORE EXPOSURE % POWER % FLOW K-EFFECTIVE 14 318 87 7 99 4 1.00170 1
m m
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/
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E E E E E M M M M M m m m e e g g 1 FIGURE 3 30 CORE AVERAGE RXIRL TIP TRACES 81/02/16 VERMONT CYCLE 7 LPRM CALIBRRTION 521 08/08/80 CTP=1504 WT=47.8 0 k
-x- = MEASURED E
N = CALCULATED E b-8 J.
~
m r vi E i-8*- l l O k i 8
- 1'.50 1 75 '2'.00 2'.25 2'.50 k.00 0'.25 0'.50 0'.'15 l'.00 1'.25 BOTTOM OF CORE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE
' 14.972 94 4 99.6 1 00505
M M 1 4 6 1 4 4 M 1 2 M M. R H
. /
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. M 6 3 3 0 3 3 2 / 3 3 3 . 3 .
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.'T 3 P R n E E 3 E S i S W E O 1 M R U
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I FIGURE 3.52 I VERMONT YANKEE CYCLE 1A COMPARISON OF SIMULATE AND PROCESS COMPUTER EOC BUNDLE AVERAGE EXPOSURES (MWD /ST) VT202 VT205 VT224 VT227 YT240 VT271 VT147 VT047 VT076 VT333 VT158 3513.2 3636.0 4005.9 3967.4 3744.7 3923.1 4101.5 3975 4 3489.0 3084.5 2175.4 3818.9 3701.0 3738.5 37E0.7 3819 6 3957 7 3909 2 3851.7 3587.4 3233.4 2291 5 105 7 65 0 -?.7.4 -206.7 14 9 34 6 -132.3 -123.7 98.4 148 9 116.1 VT231 VT234 VT258 VT257 YT138 vT043 VT370 VT341 VT163 VT196 VT201 3759.0 4223 4 4028.3 3665.2 3940.8 4276.5 4041.9 3527.5 2328.7 2222.6 3495.7 4122 0 3823.C 3540.E 2443.9 2322.E 3499 0 3907.7 3954.0 3675 3 3720.0 4123.4
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-36.9 VT056 3387.1 VT302 2566.3 VT309 2307.1 VT308 2133.9 3596.6 3618 4 3662.7 3319.7 2796.1 2500.7 2230.9 135 8 114.4 122 5 -67 4 229.8 193 6 97 0 VT075 VT069 VT109 VT320 3170.2 3213.7 3128.9 2642.1 I 3287.6 117.4 VT331 3357.1 143 4 VT321 3152 1 23.2 VT322 2737.3 95.2 BUNOLE 10 I 2252.6 2340 0 87.4 2200.5 2351 9 91.4 2167.2 2205 0 37.8 PROCESS ConPUTER SinULATE 01FFERENCE I 87 I
I FIGURE 3 53 I VERMONT YANKEE CYCLE 2 COMPARISON OF SIMULATE AND PROCESS COMPUTER EOC BUNDLE AVERAGE EXPOSURES (MWD /ST)
' VT158 VT202 VT205 VT219 VT250 VT240 VT271 VT147 VT047 VT333 GE0033 8251 1 8328.6 9672.3 9924.6 9304.9 9143.6 9566.8 9427.4 8271 1 6E52.1 2311.7 8774.0 8825.4 8916 2 9007.6 9492 8 9324.9 9314.8 9166.4 8671.2 6707 5 28S0.9 522 9 496.8 -756 1 -917 1 187 9 101 3 -252 0 -261 0 400 1 155 4 549.2 VTt63 VT036 VT206 VT029 VT234 VT112 VT251 VT028 VT043 VT370 GE0028 1536.9 8288.3 9558.4 8280.3 8211.5 8205.0 9584.3 8686 4 1955.0 6582.8 2243.9 8037.0 853S.2 8890.2 80E3 2 8610.2 8378.8 9326 2 8699.7 8420 0 6707.6 2731.7 500 1 250 9 -668 2 -217.1 398 7 173 8 -258 1 13.3 465 0 124 8 487.8 Vil67 VT200 VT199 VT233 VT232 VT256 VT121 VT140 VT092 VT319 VT342 8711.9 9890.3 8854 9 8247.6 8811.5 9543.1 9394.0 8883.0 7513.7 5903.4 4482.9 8099.7 8834.5 8992.3 8555.2 8612.0 9312.0 9028.1 8789 3 8324.7 6267.7 4836.5 I _ -612 2 VT175
-995.8 VT064 137 4 VT212 307 6 VT373
-199 5 VT239
-231 1 VT076
-355 9 Vit31 9248.6
-93.7 VT038 8801.0 811 0 VT037 7748.8 384.3 VT347 6092.3 353 6 9841 6 8705.1 9007.6 8172.4 9502 1 8478.0 9032 4 8384.1 9134.7 8250.3 9263 8 8542 4 9065.9 8907.0 7686 6 605E.7
. -809.2 -321.0 127.1 77.9 -238 3 64.4 -182 7 106.0 -C2.2 -35.6 VTl74 VT211 VT357 VT356 vf241 VT006 VT005 VT299 GE0027 9744.5 9520.5 9406.9 9558 0 9525.4 9263.5 8874.5 7760.4 2779.2 l' 9188.4
-556 1 9192 0
-338 5 9205 8
-201 1 9304.5
-253 5 9250 7
-274.7 9130.7
-132 8 vf055 8898 9 24.4 7 5 2 4 .~.
-235.7 3462 0 622 8 DE0003 VT268 VT109 V1358 VT075 VTott VT136 VT295 I 9137.8 8854.4
-283.4 9004.6 8421 0
-583 6 9506.1 9314.0
-192 1 8199.1 8432 0 232 9 8998.6 8808.3
-190 3 8502.3 8529.2 26 9 9102.0 8758.0
-344.0 6941.4 6839.2
-102.2 2359 9 2832 4 472 5 VT365 VT279 VT281 VT117 VT010 VT156 vil26 VT294 OE0060 I 8801.8 8765.2
-36 6 9366.4 9208 9
-157.5 9831 1 9146.7
-684.4 9140.8 8686.4
-454.4 8556.5 8520.0
-36.5 9148.0 8726 5
-421 5 7302.9 8163 2 860.3 5922.3 6026 6 106.3 1779.3 2319 2 539 9 Vil20 VT063 VT151 VT108 VT302 VT309 VT308 VT310 9021.3 8436.9 9217.9 8969.4 7931.2 7203.9 5975.1 5604.4 9016 3 8542.4 8808 7 8784 0 7411 5 6782.2 5996.5 5575.8
-5 0 105.5 -409 2 -185 4 -519.7 -421 7 21 4 -28.6 VT046 VT050 VT103 VT056 DE0055 OE0034 GE0046 8004.6 7881.5 7932.1 8175.9 1769.7 2585.3 1935 7 8642 0 8494 2 8390.3 7641.6 3450.7 2886 4 2379 9 444 2 I -534.3 637 4 602 7 458.2 1681 0 301 1 VT331 VT069 VT344 VT320 6366 1 7260.1 6446.0 6568.9 6781.0 7372.7 6298.8 6041.0 I 414 9 GE0043 312.6 GE0030
-147 2 VT322
-527 9 BUNOLE 10
, 2287.2 2330.1 4502.8 PROCESS COMPUTER 2901.3 2729 6 4848 2 StrutATE 614 1 399 5 345.4 O!FFERENCE 11 ee I
I FIGURE 3.54 I VERMONT YANKEE CYCLE 3 COMPARISON OF SIMULATE AND PROCESS COMPUTER EGC BUNDLE AVERAGE EXPOSURES (MWD /ST) I LJ945 LJ795 LJ1056 LJ763 LJ938 LJ822 LJ1054 LJ1074 LJ887 LJ778 DE0033 11213.9 11039.8 11560.3 11899.3 11381.6 10984.0 10521.5 10287.0 9S58.4 8897.1 8669.8 11362.0 11162.2 11193.4 11492.0 11458.6 11179.2 10864.9 10530.1 9662.6 8187 9 8444.4 122 4 -407 3 '195.2 243.1 -295.8 -709.2 -225.4 I 148.1 -366 9 77.0 343 4 LJ975 LJ1017 LJ886 LJ1032 LJ789 LJ892 LJ1004 LJ1048 LJ777 LJ876 GE0020 10905 8 10844.9 11519.3 11813 1 11236.4 10995.0 10542.5 10184.8 9859.9 8663.0 8170 8 11174 2 11070.8 11112 5 11411.4 11295.1 11201 8 10866.8 10477.4 9510.4 7894 9 7583.2 I 268.4 LJ825 225.9 LJ879
-406 8 LJ985
-401.7 LJ902 158.7 LJ1026 206.8 LJ1071 324.3 LJ883 292 6 LJ845
-349.5 LJ1044
-768.1 LJ882 7072.4
-190.6 LJ986 11359.3 11265.1 11210.6 11452.4 11723.0 11509.4 10609.3 10279 0 8350.6 4082.1 11194.6 11073.8 11105 3 11401.8 11365.5 11142.0 10736.0 10206 4 9029.8 7063.7 4560.0
-164 7 -191 3 -105 3 -50 6 -357.5 -367.4 126.7 -72.6 679 2 -8.7 477.9 LJ926 LJ847 LJ977 LJ888 LJ894 LJ1047 LJ840 LJ987 LJS44 LJ756 11662.4 11341.4 11319 6 11564.9 11706.6 11381 6 10261 0 9674.3 7932.0 5862.1 11456 8 11226 0 11221.7 11490.9 11404.3 11092.6 10559.3 9777.1 8072.0 5859.8
-205 6 -115 4 -97 9 -74 0 -302.3 -289 0 298 3 102 8 140.0 37.7 LJ890 LJ762 LJ842 LJ870 LJ895 LJ792 LJ1042 LJ820 GE0027 I 11568.8 11487.2
-81 6 11351.4 11252.9
-98.5 10704.1 11209.8 505 7 10960.3 11397.3 437.0 10452.0 11238.7 786.7 10005.3 10843.1 837 8 9878.6 10170 0 291 4 9101 9 9040.7
-61.2 9401.8 10348.9 947.1 LJ776 LJ850 LJ1078 LJ1072' LJ1C81 LJ878 LJ1018 LJ1058 GE0003 I 11391.3 11453 6 62 3 11416.1 11333 1
-83.0 10617.6 11238.1 620 5 10649.9 11218.1 568 2 10237.3 10945 5 708 2 9746.4 10485.6 735.2 9407.9 9662.2 254.3 8451.8 8300.9
-150 9 8366.5 8689.1 322.6 LJ1033 LJ1063 LJ852 LJ829 LJS42 LJ768 LJ1000 LJ791 GE0060
, . 10683 0 10477.5 11445.4 11115.5 9792.0 9352.9 8123.2 7245.5 10430.8 l 11171.9 11049.8 10879.8 10709 5 102S3.4 9656.7 86s6.7 7027 2 7198 7 488.9 572 3 -565.6 -406.0 501 4 343 8 573.5 -218 3 -3232 1 LJ1003 LJ1037 LJ859 LJ760 LJ1069 LJ1027 LJ1041 LJ1046 , 10313 8 10075.8 10940.3 10430.8 9054.8 8450.9 7281.6 5713 2 i 10667.0 10531.4 10239 3 9846 5 9103 9 8337 9 7039 3 5387.4 353 2 455.6 -701 0 -584 3 49 1 -113 0 -242 3 -325 8 LJ1001 LJ786 LJ1031 LJ896 DE0055 GE0034 DE0046 9805.6 9748 1 8396 1 8028.9 9908.3 8827.4 6508.9 9738.5 9528.6 9036.4 8111 6 10386.3 8774 1 7278.8
-67 1 -219 6 640 3 82 7 478.0 -53 3 769 9 LJ800 LJ1073 LJ907 LJ1038 8161.6 8508.5 7181.4 5971.9 l 8228 5 7929 4 7092 0 5931 8
-433 1 -579.1 -89 4 -40 1 DE0043 DE0030 LJ991 BUNDLE 10 t
8504 5 8194.8 4008.2 PROCESS ConPUTER 8506.1 8004.7 4583 7 SIMULRTE 16 -190.1 575 5 01FFERENCE 89 ll
FIGURE 3 55 I VERMONT YANKEE CYCLE 4 I COMPARISON OF SINJLATE AND PROCESS COMPUTER EOC BUNDLE AVERAGE EXPOSURES (MWO/ST) LJ1046 LJS13 LJ3964 LJ887 LJ3959 LJ944 LJ3955 LJ1048 LJ3953 LJ3862 GE0033 12890.1 14407.0 9415.5 18378.5 9604.4 16135.1 8861 4 17651.3 8382 8 7625.9 13135.9 13423.5 14956.5 9008.7 17794.9 9328.5 16243 1 9123 1 18163 3 8244.5 7177.1 1271E.4 533 4 549 5 -406.8 -583.6 -275.9 108.0 261.7 512 0 -138.3 -448.8 -419.5 LJ1041 LJ878 LJ1073 LJ986 LJ820 LJ833 LJ1058 LJ3870 LJ1018 LJ38S3 GE0028 14597.6 16909.5 16990.8 13038.3 17432.0 17930.0 16268 1 8613 1 16574.5 7386.5 12444.4 15082 1 18370 0 16002.9 13067.3 17214.5 17670.5 16341.6 9014.0 16703 1 6816.5 11925.6 484 5 1460.5 -987.9 29 0 -217.5 -259.5 73.5 400 9 128.6 -570.0 -518.6 LJ3970 LJ876 LJ3943 LJ1038 LJ3960 LJ882 LJ3878 LJ987 LJ3865 LJ871 LJ1004 9557.8 17155.5 9033.4 14617.5 9148.6 15178.8 8787.6 16781 8 7458.0 16728.5 13455.9 9116 0 15964.2 9238.0 14268.8 9346.3 15306.4 9246 2 17273.8 7738.5 16002 5 14135.7
-441 8 -1191.3 204.6 -348.7 197.7 127.6 458 6 492.a 280.5 -726.0 683 8 LJ1053 LJ991 LJ756 LJ865 LJ778 LJ3885 LJ845 LJ3871 LJ840 GE0027 18161.3 12839.8 14319.9 16501.8 16661.0 8899.8 17544.5 7736.1 16326 8 14041.8 I 18E84 9 523 6 LJ3571 12955 8 116 0 LJ1069 14134.4
-185.5 LJ3965 16763.9 262 1 LJ800 16189.7
-471 3 LJ3961 9335.1 435 3 LJ1044 17879 4 334 9 LJ3879 8340.0 603 9 LJ1074 16424.5 87 7 GC0060 14472 9 431.1 9325.0 17058.0 9260.4 16617.8 9845.0 16971 3 8452.3 17081.5 10999.4 9280.J 17173.9 9242.9 16244.8 9071.7 16878 6 8657.0 17119.1 12274.3
-44.7 115.9 -17.5 -373 0 -773.3 -92.7 204.7 37.6 1274 9 LJ896 LJ786 LJ907 LJ3892 LJ1031 LJ3886 LJ792 LJ3872 GE0003 16249.3 17713.0 15605.9 9347.1 17253.8 9735.9 16961.3 7246.3 12440.6 16430.5 17753.9 15406.1 9547.0 17037.7 8965.7 17898.0 1031.3 12957.0 181.2 40.9 -199.8 199 9 -216.1 -770 2 936.7 -215.0 516 4 LJ3972 LJ1027 LJ3896 LJ982 LJ3889 LJ1081 LJ3880 LJ3873 LJ1042 9432.1 16674.8 9344.5 18492 3 8465.1 17054.5 7273.8 6243.7 12785.1 9346.3 16468.S 9366.1 18094.0 8877.1 18032.8 7503.7 6072.0 13741 6
-83.8 -206.0 321 6 -398 3 412 0 978.3 229 9 -171.7 956.5 l LJ1037 LJ3899 LJ760 LJ3893 LJ817 LJ3887 LJ3881 LJ1047 17892.3 8921.3 17619.3 7980.6 16964.8 7006.1 6235.9 15354.4 18272.7 9012 7 17342 7 8424.6 16432.8 7083.5 6088 8 15193.5 380 4 91.4 444.0 77.4 -147.1 -160 9 I
-276.6 -532 0 LJ3973 LJ768 LJ3897 LJ829 OE0046 CE0034 LJ942 6598.4 16634.5 7307.3 18985.0 11188.1 128S2.4 12606.4 8267.4 16711.3 7712.3 16585.1 12394.0 13065.9 13871.0
-331 0 76.8 405.0 -399.9 1205 9 203 5 1264.6 LJ3902 LJ3900 LJ981 GE0055 7790.5 7519 6 15894.3 14379.3 I 7187.4
-603 1 DE0043 6815.3
-703.3 GE0030 15865.8
-28.5 LJ1063 14516.3 137 0 8UNOLE 10 I 13031.5 12775.4
-256 1 12457.6 11947.0
-513 6 13407.4 14312.3 904.9 PR02ESS ConPUTER SIMULATE DIFFEREN2E
~
90
I FIGURE 3 56 I VERMONT YANKEE CYCLE 5 COMPARISON OF SIMULRTE AND PROCESS COMPUTER EOC BUNDLE AVERAGE EXPOSURES (MWD /ST) I LJ774 LJ3981 LJ879 LJ3963 LJ954 LJ3971 LJB39 LJ3960 LJ847 LJ3956 LJ902 16085.8 14899.6 17441 3 15860.0 17255.8 16s19.3 18083.8 16071.8 16966.0 15120.6 14497.4 16846 2 15210.9 17377.1 15836.0 17343.9 16417.8 17579 9 16121.4 16769.5 14270.7 14470.7 760.4 311 3 -64.2 -24 0 88 1 98 5 -503.9 49 6 -196 5 -849 9 -26.7 LJ3953 LJ3949 LJ7043 LJ3884 LJ7041 LJ3907 LJ7039 LJ3881 LJ7051 LJ3872 GE0028 14693.5 15309.9 7173.5 15736.9 7412 2 15970.5 1577.5 13448 6 6543.6 12534.2 15328.8 15056.5 16148.3 7404 2 16355.5 7496.6 16184.9 7530.2 13148.5 6486.2 12199 4 14749.4 363 0 838 4 230.7 618 6 84.4 214.4 -47 3 -300 1 142 6 -334.8 -579 4 LJ1017 LJ7029 LJ1056 LJ7067 LJ1009 LJ7142 LJ1055 LJ7053 LJB95 LJ3864 GE0033 17754 3 7927.5 18255 8 7700.9 17499.8 7388.3 17359 5 6970.6 15400.4 11869.8 15335.6 17272 1 7418.4 17559.5 7393.3 17567 5 7505.5 17485.4 7039 2 16530.5 12343 0 15179 3
-482 2 -509 1 -696.3 -307 6 87 7 117 2 125.9 68.6 1130 1 473 2 -156.3 LJ3955 LJ3892 LJ7073 LJ1026 LJ7138 LJ3932 LJ7055 LJ3967 LJ3888 LJ1032 16379 1 17033.8 7747.9 18636.5 7324.1 15033.3 7112.4 15776.5 13499.8 15109.8 16091 4 16702.7 7547.0 17793.6 7461 8 14458 1 7236.6 15704 2 14117.8 14826.4
-287 7 -331 1 -200 9 -842 9 137.7 -575.2 124 2 -72.3 618.0 -283.4 LJS75 LJ7030 LJ977 LJ7134 LJ1014 LJ7059 LJS31 LJ3896 CE0060 I 17438.8 175S2.0 123.2 1521.6 7749.5 227.9 18030.0 17801.7
-228 3 7419.2 7552 1 132 9 18259.3 17755.3
-504 0 7230.3 7354 3 124 0 17433.5 17080.3
-353 2 14909.0 15194 1 285 1 14538 1 16039.4 1501.3 LJ3958 LJ3870 LJ7074 LJ3861 LJ7063 LJ789 LJ3863 LJ3880 OE0003 I 16874.8 16656.9
-217.9 15844.4 16411 0 566 6 7739.4 7757.2 17.8 15098 4 14631 7
-466.7 7393.0 7489 8 96 8 17436.0 17493 3 57 3 13652.0 13177.1
-474 9 12766.b 12850.0 83 5 15470.0 16039.9 569.9 LJ962 LJ7031 LJ1033 LJ7069 LJS85 LJ3882 LJ762 LJ3893 GE0027 18905.5 8332.3 17343.8 7410 1 17455.5 13543.8 15538.0 11885.9 16225 5 17668.0 7752.8 17642 0 7443 3 17197 5 13465.3 16265 0 12876.6 16918.1
-1237.5 -579 5 298 2 33 2 -258.0 -78 5 727 0 990.7 692 6 LJ39E9 LJ3866 LJ7075 LJ3965 LJ3878 LJ3911 LJ3868 LJ1050 17154.0 13973 8 7115.5 15780.0 14911 5 13034 1 11648.6 13821 1 16041.5 13192 0 1100.6 15708.7 15154.0 13080.4 12807 0 14284.7
-1112 5 -781 8 -14.9 -71 3 242 5 46.3 1158 4 463.6 LJ842 LJ7077 LJ1072 LJ3879 DE0046 OE0034 DE0055 16809.5 6697.1 15407.6 13305.3 14764.3 15896.4 16645.8 16820.4 6509.5 16507.0 13960.4 16194.6 16166.8 16970.7 16.9 -187.6 1099 4 655 1 1430.3 270 4 324 9 LJ7019 LJ3900 LJ3886 LJ1020 5919.4 13102.0 13831.8 14322.5 5397 2 12006 8 13529.8 14793 3
-522.2 -1095.2 -302 0 470.8 LJ850 CE0030 GE0043 BUNDLE 10 I 14556.4 14418.6
-137.8 15337.4 14777 0
-560.4 15294.6 15230.5
-64.1 PROCESS COMPUTER S inUL RTE 01FFERENCE I 91 I .
FIGURE 3 57 VERMONT YANKEE CYCLE SA I COMPARISON OF SIMULATE AND aROCESS COMPUTER E0C BUNDLE AVERAGE EXPOSURES (MWD /ST) i LJ0899 LJ7051 LJ1010 LJ0780 LJO991 LJ8721 LJ3873 LJ8712 LJ3924 LJ70E9 DE002S 17313.0 13502.6 17920.5 16703.8 18050.3 7936.8 20942.0 7791.2 19482.5 12835.4 18135.0 17860.5 13802.1 17551.0 16643 0 18377.7 8069.1 20028 2 7821 2 19520.5 13104.1 17692.4 547.5 299.5 -369.5 -60.8 327.4 132 3 -913 8 30.0 38 0 268.7 -442 6 LJ7077 LJ3869 LJ7113 LJ1059 LJ7062 LJ0805 LJ7058 LJ0814 LJ7079 LJ7038 LJOBB3 13503.6 22517.3 7562.4 17050.8 7705.6 18080.8 8162.8 16217.0 12237.3 12794.8 17166 0 13627.5 23448.5 7612 4 17976 3 7796 5 18558.3 7990.9 17338.6 12086 1 13081.8 17324.4 123 9 931 2 50 0 925.5 90 9 477 5 -171 9 1121 6 -151 2 287 0 158 4 LJ1083 LJ7102 LJ3861 LJ7116 LJ3879 LJ8722 LJ7029 LJ8713 LJ0765 LJ7074 GE0033 18161.3 7750.4 21399.8 7554.2 21177.3 8564.5 15360.9 7319.0 15467.0 12124.8 17341.0 17647.8 7574 1 21373.0 7778 4 21142 1 8142 5 15206.5 7565.9 16306.3 12706.5 17586.8 I -513 5 LJ0857
-176 3 LJ0864
-26 8 LJ7123 224 2 LJ3994
-35 2 LJ8726
-422 0 LJ1019
-154.4 LJ8716 246 9 LJO900 839 3 LJ7142 581 7 LJO999 245.8 16870.8 17132 8 7747.6 21847.3 6634.4 18529.3 7626.9 lb948.5 12451.3 14776.0 16571.6 17579.5 7807.9 22231.3 8054.7 18116.0 7805.6 16216.4 13183.9 15087.8
-299.2 446 7 60 3 384 0 -579.7 -413 3 178.7 267 9 732 6 311 8 LJO986 LJ7098 LJ5863 LJ8730 LJ1029 LJ8723 LJ7046 LJ7070 LJ0791 18558.5 8053.3 21251.0 8659.3 18963.5 7977.3 14096.1 13132.0 16162.9 18410.9 7827.0 20277.7 8083.6 18822 9 7811 5 14729.5 13417.9 17014.5
-147.6 -226.3 -973.3 -575 7 -140 6 -165.8 633.4 285.9 851 6 LJ8738 LJ0766 LJ8734 LJ0848 LJ8727 LJ0779 LJ3867 LJ7055 LJ0921 8204.9 19377.8 8698.0 18423.3 8165.4 19179.5 18444.3 12548 1 18585.5 8117.0 18882.8 8207.5 18120 2 7846 0 18665 1 18365.6 12923.4 17607.0
-87.9 -495.0 -490.5 -303 1 -319.4 -514.4 -78 7 375 3 -978 5 LJ3571 LJ7110 LJ7043 LJ8731 LJ7030 LJ3865 LJ8717 LJ7138 I
GE0060 19455.0 8545.6 15527.5 8553.5 14446.1 18013.0 5300.6 11597.3 16593.8 19933 2 8022.2 15221.0 7846.5 15001.1 18495.0 6158.8 12337.8 1848S.6 478 2 -523 4 -306 5 -707 0 555 0 482.0 858.2 740.5 1892.8 LJ8739 LJ0803 LJ8735 LJO983 LJ7053 LJ7056 LJ7134 LJ0891 8087.3 16634.5 8252.0 16486.3 13284.3 12907.9 11751.5 14758.6 7757.6 17196 2 7539 3 16184.2 13340.0 13036.3 12427.9 15908.5
-329 7 561.7 -712.7 -302 1 55.7 128 4 676 4 1149 9 LJ3875 LJ7101 LJO914 LJ7087 LJ1041 LJ0849 GE0046 19440.5 6702.7 17776.8 13106.1 16574.8 18551 0 16896.8 19271.E 6818.5 17682.2 13221.3 17141 6 17648.8 18629.0 I -169.0 LJ709E 12932.4 115 8 LJ7037
--94.6 LJ7067 115 2 LJ0888 566 8 -902 2 1732.2 13650.9 12360.8 15003.9 13103.1 13245.0 12327 9 15065 3 170.7 -405 9 -32.9 61 4 DE0030 LJ0852 DE0043' BUNOLE 10 I
18183.0 18099.8 17331.5 PROCESS COMPUTER 17681 9 17459.5 17611.3 SinULATE
-501 1 -640 3 279 8 DIFFERENCE ll e2 ll L_ .< _
I FIGURE 3 58 I VERMONT YANKEE CYCLE 7 COMPARISON OF SIMULATE AND PROCESS COMPUTER E0C BUNDLE AVERAGE EXPOSURES (MWD /ST) LJ3914 LJ7123 LJ7030 LJ7098 LJ7029 LJ7058 LJ7051 LJG931 LJ3981 LJ765 LJ7102 14941 0 24961 0 14941.0 21289.0 15402.0 22310.0 15293.0 19719.0 5896.0 21338.0 21210.0 15172.2 19954.7 5578.4 21708.6 22229 4 15183.0 25051 8 15512 7 22158 9 15510.5 22181.1 242 0 90 8 571.7 869.9 108 5 -128 9 -126 8 235 7 -317.6 370.6 1019 4 I LJ7113 14563 0 LJ7079 19005.0 LJH004 7677.0 LJ999 21106.0 LJH024 7867.0 8063 0 LJ891 21237.0 22365.3 LJO967 7959 0 7802.8 LJ3956 24534.0 23728 2 LJG939 6946.0 6790.2 LJB726 14321.0 13531.2 LJ3924 22270.0 22488.3 14909.5 19286.2 8027.5 21698.0 346.5 281.2 350 5 592 0 196 0 1128.3 -156 2 -805 8 -155 8 -769.8 218.3 LJ7087 LJ8735 LJ7138 LJS739 LJ7038 LJO951 LJ8731 LJ8734 LJ3863 LJ3902 LJHOIO 8084.0 20652 0 16606.0 19232.0 16396.0 204E9.0 8130.0 14693 0 13731.0 23301.0 24933.0 7408.9 14314.0 13200.5 22924.4 I 24496 8
-436.2 LJ7116 7975 3
-108 7 LJ888 20613.1
-38 9 LJ8713 15653 1
-952 9 LJ7056 19830.5 598.5 LJG379 15745.3
-650 7 LJ7070 20185.5
-283.5 LJG963
-721 1 LJ7067
-379 0 LJO935
-530.5 LJ3865
-376.6 20656.0 8779 0 20772.0 8449.0 19322 0 589$.0 21641.0 I 15179.0 15389.5 210.5 LJ7046 21836.0 21744 8
-91 2 LJH016 15890.0 15802.8
-87 2 LJ7134 20727.2 LJG995 71.2 8460.7
-318 3 LJ7055 20859 5 87.5 LJ8727 7843.8
-605 2 LJ7069 18813 1
-508 9 LJ0947 5767 6
-127.4 LJ3915 220S7.8 426 8 I 21048.0 21898.9 850 9 8034.0 8228.0 194 0 19877.0 19920.0 43 0 9089.0 8532 8
-556 2 19986 0 20524.3 538 3 16184.0 15819.6
-364.4 19830.0 19965.7 135.7 7109.0 6584.9
-524 1 19532.0 20496 0 964.0 LJ3888 LJ7062 LJ983 LJ8712 LJ7053 LJ8723 LJ7142 LJO983 LJ8738 15118.0 22844.0 16523.0 21157.0 15874.0 19363 0 7417.0 14630.0 20453.0 l
15521 4 22776.4 15920.0 2C839.8 15809.6 20271 8 7248.5 14099 5 20910.5 403 4 -67 6 -603.0 -317 2 -64.4 908 8 -168 5 -530.5 457 5 l LJ7043 LJH012 LJ7037 LJG991 LJ7096 LJG971 LJ8717 LJO943 LJ3875 22419.0 7993.0 20729.0 7741.0 19837.0 7276.0 11865.0 5612.0 22259.0 22221.1 7864 0 20398 3 7883.7 19979 8 7255 0 12671.7 5171 2 22174.5
-197.9 -129 0 -330 7 142.7 142 8 -21 0 806.7 -440 8 -84.5 LJ3982 LJO999 LJ7074 LJG975 LJ8721 LJG955 LJ7101 LJ7110 15566.0 25171.0 7407.0 18435.0 6530.0 14178.0 5564.0 10943.0 15203 8 25099 3 7423.5 19166.1 6591.3 14058.8 5169 3 10872 3
-362 2 -71.7 16 5 731.1 61 3 -119 2 -394 7 -70.7 LJ7017 LJH000 LJB716 LJO987 LJ3897 LJ3921 LJ3959 19639 0 6771.0 13792 0 5858.0 20054.0 20464.0 22337.0 19801.2 6789.7 14285.5 5770 9 20546.4 21681.7 22720.8
,I 162 2 LJG959 18 7 LJ8730 493.5 LJ8722
-87 1 LJ3867 492 4 1217 7 383.6 5864.0 14272.0 13603.0 22047.0 5574 6 13558.2 13147 1 21951 9 I. -289 4 LJ3960
-713 8 LJ3871
-455.9 LJ3873
-95.1 BUNOLE 10 I 22187.0 22473 3 286.3 22246.0 22882.7 636.7 23005.0 22686 9
-318 1 PROCESS COMPUTER SIMULATE O!FFERENCE 93
FIGURE 3 59 QUAD CITIES UNIT 1 CYCLES 1 AND 2 CORE DESIGN AND OPERATING DRIA FROM EPRI NP-240 9
. PERCENT OF CORE POWER 8
5 S-8 h' x 28-
? to x
O!
- ci s LEGEND I
u i CYCLE 1
$=- 9 CYCLE 2
- a. ;
8 5-8 a
*0.00 2'.00 4'.00 6'.00 8'.00 1'0 00 l'2.00 l'4.00 l'6.00 1'8 00 2'0 00 CORE AVERAGE EXPOSURE, GWD/T
FIGURE 3 60 QURD CITIES UNIT 1 CYCLES 1 AND 2 o CORE DESIGN AND OPERATING DATR FR0t1 EPRI NP-240 9
;. PERCENT OF CORE FLOW 8
8 J 8-L 8E g & u 88 g- g g LEGEND i CYCLE 1 E CYCLE 2 a_
- g. -
8 a
'*0.00 2'.00 4'.00 8'.00 8'.00 l'O . 00 1'2.00 l'4.00 l'6.00 l'8.00 2'0.00 CORE AVERAGE EXPOSURE, GWD/T
FIGURE 3 61 QURD CITIES UNIT 1 CYCLES 1 AND 2 o CORE DESIGN RND OPERATING DATR FROM EPRI NP-240 ,
'9 ; 2. CONTROL R00 NOTCHES INSERTED 8
o-
~}o ,
m 8 a c-o w 6-5o m9 F 28.- 8 m w
.o u9 bo o
LE0END Eg ad. 1 CYCLE 1 9 CYCLE 2 z co u9
?-
8 S .00 2 00 4 00 6.00 11 . 0 0 10.00 1k.00 14.00 16.00 16.00 20.00 CORE AVERAGE EXPOSURE, OWO/T
m m m m m m m W W - M M M M M M M FIGURE 3 62 QUA0 CITIES UNIT 1 CYCLES 1 AND 2 CORE DESIGN AND OPERATING DATA FROM EPRI NP-240 AVERAGE RELATIVE WATER DENSITY 8 a-C
<n 2E da-5 b
z- g
'S $'
$8 wo-ac '
w iuGEND o Eo 5"- g i CYCLE 1 , g 9 CYCLE 2 ' e a-2 k.00 2'.00 4'.00 8'.00 8'.00 1'0.00 t '2 .00 l'4 00 l'6.00 t '8 . 00 2'0.00 CORE AVERAGE EXPOSURE, GWD/T
._m.
M M M M M M M M M M M M M M M M M M FIGUllE 3 63 OUAD CITIES UNIT 1 CYCLES 1 r.dD 2 CORE DESIGN AND OPERATING DATA FROM EPRI NP-240 8
- f. CALCULATED INLET SUBC00LIND 8
b-co 29 38' O o O
$8 EJ.*
g s w a
*8 .,
- d. f s
cc LEGF TID
$8 a"d- i CYCLE 1 m 9 CYCLE 2 O
8 L 8 L T.00 2'.00 4'.00 6'.00 8'.00 1'O .00 l'2.00 1'4.00 l'6.00 l'.00 8 2'.00 0
. CORE AVERAGE EXPOSURE, OWD/T
~ ~' ' ~ '
~
y .y y y y g m m m m m m q m m m m y FIGURE 3.64 QUAD CITIES UNIT 1 CYCLES 1 AND 2 CORE DESIGN AND OPERATING DATR FROM.EPRI NP-240 E CALCULATED K-EFFECTIVE E E U l X- - u9 e W~' u w Y , ---- 2.J g-dm / [ LEGEND uS i CYCLE 1 d~ u 9 CYCLE 2 E a-E.
%.00 2'.00 4'.00 e'.co a'. co t'o . 00 1'2.00 t'4 00 t's .co t's .oo 2'o.00 CORE AVERAGE EXPOSURE, GWD/T
FIGURE 3.65 CORE AVERAGE AXIAL TIP TRACES 81/03/07 QUAD CITIES 1. CYCLE 1. DATA SET 02 AUGUST 30,1972. A SEQUENCE S h-o -x- = MEASURED N' - = CALCULATED 8 d-8
.A
~
- 8. x 8
b-8 s-S k oe
%.00 0'.25 0'.50 0'.75 1'.00 l'.25 l'.50 l'.75 2'.00 2'.25 2'.50 BOTT0t1 0F CORE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE l .646 89.7 101.6 .99639 i
FIGURE 3.66 CORE AVERAGE RXIAL TIP TRACES 81/03/07 QURO CITIES 1. CYCLE 1 DATA SET 08 JUNE 6, 1973. 8 SEQUENCE r g. l g -x- = MEASUhuo 2 = CALCULATED e. 8 -
)
{ x 8 i-8 k k 3 .00 0'.25 0'.50 0'.75 l'.00 l'.25 1'.50 l'.75 2'.00 2'.25 2'.50 80ITON OF CORE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE 3.696 92.4 96.7 99672
.ll e - m M M M M M M M M*M M M M M M M M M FIGURE 3 67 CORE AVERAGE AXIAL TIP TRACES 81/03/07 QUAD CITIES 1, CYCLE 1. DATA SET 15. MARCH 5, 1974. A SEQUEi,i'E 8 5-
. i
'I -x- = MEASURED o l 9 N- = CALCULATED S d- \ 8 5-5
- 8 i-8 2
8 k 8 i .00 0'.25 0'.50 0'.75 l'.00 l'.25 1'.50 l'.75 2'.00 2'.25 2'.50 80TTOM OF CORE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE 6.948 87 1 99 7 1.00113
;.6 M W. M M 'M W W W m a e M m m e e e e FIGURE 3.68 CORE AVERADE RXIAL TIP TRACES 81/03/07.
QUAD CITIES 1. CYCLE 2. DATA SET 18 AUD. 15, 1974. A SEQUENCE S 5-
-x = MEASURED 8 * = CALCULATED u
to f_ 8 i- r u r 8 5- , 8 k M. 8
%.00 0'.26 0'.50 0'.75 l'.00 l'.25 1'.50 l'.75 2'.00 2'.25 2'.50 BOTTOM OF CORE l
CORE EXPOSURE */. P O W ER % FLOW K-EFFECTIVE 6.752 86 5 85.6 .99704 (
FIGURE 3 69 CORE RVERAGE RXIRL TIP TRACES 81/03/07 QURD CITIES 1. CYCLE 2. DATR SET 22. DEC. 11, 1974. B SEQUENCE 8
.f
-x- = MEASURED g
-- = cal.CULATED N'
c-a 8 1 k 8 5- , 8 s-8 k 8 1'.00 l'.25 1'.50 l'.75 2'.00 2'.25 2'.50 i .00 0'.25 0'.50 0'.75 80TT0t1 0F CORE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE 8.213 99.6 98.7 .99993
FIGURE 3 70 CORE AVERAGE AXIAL TIP TRACES 81/03/07 QURD CITIES 1 CYCLE 2. DATA SET 28. DECEMBER 19, 1975. ARO. C0AST DOWN 8 J. N
-x- = MEASURED g
C- - = CALCULATED 8 u 8 J. 8 x 8 L a 8 k 8 n k e 1 8
*b .oo o'.2 s o'.so o'.75 1'.00 t'. 2 5 t'. 5 0 t'. 7 5 2'.00 2'.25 2'.50
, BOTTON OF CORE i CORE EXPOSURE % POWER % FLOW K-EFFECTIVE 12.272 61.6 97.7 1.00068
m m .m W m M W m W W W M M m m m M M M FIGURE 3 71 UNNORr1ALIZEO TIP TRACES 81/03/07. 817 825 833 841 849 f . . . . . .
' ~
1609 161's 1625 h 1633 1641 1649 I ' 2409 2417 2425 2433 2441 2449 2457
)
- a. >>.,, .
3209 3217 3225 3233 3241 3249 3257 5 e % I , , , , I .. .,, ,,,,, 4009 4017 4025 4033 4041 4049 4057 N
, .. . ...ii ,
I,,,,, 4809 4817 - 4825 4833 % 4841 D 4849 I - . .,,, 5625 % 5633 SG41 AVE Y
.... . . =,.,,.
QUA0 CITIES 1. CYCLE 1. DATA SET O'2. AUGUST 30.1972. A SEQUENCE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE
.646 89.7 101 6 .99639 1
l _ _ _ _ _ _ ___ __
FIGURE 3 72 UNNORNRLIZED TIP TRACES 81/03/07. 817 825 833 . 841 . 849 P W 1609 1617 16d5 1633
~
1641 N 1649 i ! ' f . f . 2409 2417 2433 2441 2449 2467 24d5 I ' ' I 3209 3217 32d5 3233 3241 3249 ' 3257 o 7 I I /" '
. . s.
4009 4017 40$5 4033 4041 4049 .' 4057 I i 4809 4817 4825 4833 I5 4841 s 4849 l l l .. 5625 I 5633 s. 5641 lf AVE QUA0 CITIES 1. CYCLE 1. DATA SET 08 JUNE 6. 1973. 8 SEQUENCE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE 3.696 92 4 96 7 .99672
7 7 7 E 5 5 5 V 4 2 0 A 2 3 4 f 9 - 9 9 9 . 9 9 4 4 4 4 4 4 8 6 4 2 0 8 _ - 1 b 3 . 4 4 7 - . 0
/
3 E 0 C E
/ N V 1
E I 3 8 A Y U T 1 I I Q C 1 1 1 1 1 1 1 1 E E 0 4 . 4 4 4 l 4 4 4 .S f0 8 6 4 2 0 8 6 f
. 1 b 3 . 4 4 b .A E 1 K
4
.7 9 N7 1 O
^, " #
I I n 5 L9 F9 3 3 3 3 , 3 3 3 3 3 . 3 3 3 3 3 3 .H 7 8 6 4 2 0 8 6 C
. 1 b 3 , 4 4 b .R R 3 A M E 1 S N E E . O 7 R C P 8 U 5 A -
1 . G R % I F T P MI I
.T E
S I E S R T 5 . 5 5 5 , 5 5 .A - 2 2 d 5 2 d N T U - D 8 6 4 2 0 8 6 S 8 A E . 1 k 3 , 4 4 b .D O 4 Z P 9 I . X _ L . 1 E 6 A N .E E R L R O .C O N Y C N T C - U I I 7 7 7 , 7 7 .
. 7
_ 1 1 '1 1 1 1 1 8 6 4 2 0 8
. 1 k b , 4 4 S
, E I
, x T I
C 0 A U - I I Q - 9 9 9 9 9 0 d d 0 0 6 4 2 0 8 1 b b 4 4
. i n t f f Eco
M M 7 7 d 7 5 1 5 0 fA 4 2 M 2 - 3 i 4 - b. i - M N 9 9 9 9 0 . 9 . 4 4 4 4 4 4 t 0 8 M . 8 6 1 4 2 . 3 . 4 - 4 7 - 0
/ E L 3 C M 0
/ ":
* = N.
t V I I 0 4 1 u C 7 8 Y
, T u E 9 1 l 1 1 1 . - i F 9 1 1 e 41 _
4 t 4 e 4 4 ' F M 4 8 4 6 1 3 4 2 . 3 2
. 4 0
e 8 4 6 5 - A L K 4
' _ 7 W
_ M a- F 9 1 L O G. C. h . 3 3 J - 5 1
. F B 3 ,3 3 . 3 M 4 7
3 8 3 6 3 4 2 3 3 0 3 8 4 3 6 b 2G R _ , 1 2 . 3 4 U E A b. 3 - k S . o6 .M E R U G I F E C A R T
)8 5 T 1
E S P 8 P , I L s R _M ,A
,5 ,6 ,5
_ i 5 2 5 2
,5 2 2 2 2 'z T U S 2 4 2 0 8 0 A
_ D 8 6 ,3 ,4 ,4 h ,D O b
,2 P 7
_ E .1 Z . X I , , , ,
,2 L 6
- M L A 1 ,
' ,E E R
- .C t L O
R - O " ; Y C N y C N , l' _M U
?
l
, 7 1
7 1
,7 1
,7 1
,7 1
8 1 6 4 2 0 S _ B ,3 ,4 ,4 _ . 1 . 2 E I _M T I C 0 _ A . U r Q M '. 2 ' 9 9 9 9 9 0 0 0 0 0 4 2 0 8 6 4 4 1 2 3 _M
? ? ?
_M .M oe _M
FIGURE 3 75 UNNORr1ALIZED TIP TRACES 81/03/07. 817 825 . 833 841 849 Y .&. 1 ... 1609 1617 1625 k6$3 1641 1649 i i l a h . . A I_ 2409 2417 , 2425 , 24$3 h441 h449 2457 I -.
, .M .
s 3209 ' 3217 3225 % b233 3241 32[9 3257 i lI y_ a = .c 7 . 4, 1.9 s _7 y$ , 5 .
, 5 5
\ 4809 '
4817 4825 4833 ' 4841 k849 I ' I. ' ave 5625 5633 66 4 7
~.-. 3 . . .
- \
l 0U00 CITIES 1. CYCLE 2. CATA SET 22. DEC. 11. 1974. B SEQUENCE CORE EXPOSURE % POWER % FLOW K-EFFECTIVE 8.213 99 6 98.7 .99993
M M 7 7 7 E 5 5 5 V 4 2 0 A 2 3 4 M 4 M - * " 9 . 9 9 9 9 - 9 4 4 4 4 4 4 N 8 6 4 2 0 8 W
. 1 . 2 3 4 - 4 O
_M 7 0
. D T
/ S 3 A O E 0 V C
/
M 1 8 " 5 x . I 8 T 6 C0 O - 1 1 1 1 1 1 R E 0 - . 1 4 4 4 .A F 0 4 4 4 4 F 8 6 4 2 0 8 6 . E1 5 M . 1 2 3 4 . 4
.5 7 K 9
1
"
- W 7 6 -
O M " 9 1 L7 F 9 R E % 3 3 3 3 3 3 3 .B 6 3 . 3 3 3 3 . 3 3 2 0 8 6 M M 7 3 8
. 1 6 4 2 3 4 . 4 5 E
.C E
R E 6 S . .D W E E O 1 R C . P6 U A . . 8 M G I F R T
" - " " - I 2 %
" T P E I S E T 5 ,5 5 5 . 5 5 R
. 5 U 2 2 2 2 2 2 .A M 0 E
2 8 6
. 1 ,2 4 2 3
0 4 8
. 4 6
5 .T A S 2 O 7 Z D P 2 I X L
. E2 1
A 2 E M R O M . E
.L R
O
" C N " C N Y U C 7 7 7 ,7 ,7 M 1 8
. 17 6
1 4 2 1 1 0
,4 1
8 S 1
. 1 2 ,3 ,4
. E I
T I M , . . , , C
" - 0 A
U Q M 9 0 9 0 9 0 9 0 9 0 8 6 4 2 0 1 2 3 4 4 M m m Ce m
E 'E
! ! 48 !
52 ! ! .53 !
! ! 9.7 !
! ! ! .63 ! .79 !
50 ! ! '! .69 ! .84 !
! ! ! 8.2 ! 6.0 !
Relative La-140 Activity: 48 . .. ! h 1.] {
! ! 5.6 ! 7.7 ! 6.8 ! ! .6 !
- XXX & asureuent
! ! .49 ! .70 ! .85 ! ! 1.06 ! 1.10 ! XXX SIMULATE 46 ! ! .54 ! .75 ! .90 ! ! 1.09 ! 1.12 ' XX Percent. Dif ference
! ! 9.2 ! 6.9 ! 5.3 ! ! 2.8 ! 1.5 !
I ! .58 ! ! ! 1.04 ! 1.34 ! ! 1.32 ! 44 ! ! .63 ! ! ! 1.05 ! 1.33 ! ! 1.33 !
! ! 7.6 ! ! ! .9 ! -1.2 ! ! .7 !
Y ! .49 ! ! '.86 ! .99 ! ! ! 1.14 ! 1.17 ! 1.14 ! 42 ! ! ~ .53 ! ! .E9 ! 1.00 ! ! ! 1.13 ! 1.14 ! 1.12 !
~ ! ! 8.5 ! ! 2.8 ! 1.7 ! ! ! .9 ! -2.0 ! -1.4 !
w
" ! .39 ! .60 ! ! .93 ! 1.26 ! 1.11 ! 1.10 ! 1.11 ! 1.19 ! ! 1.28 !
40 ! .42 ! .63 ! ! .94 ! 1.23 ! 1.08 ! 1.09 ! 1.11 ! 1.18 ! ! 1.27 !
! 7.5 ! 6.1 ! ! 1.1 ! -2.6 ! -3.3 ! -1.1 ! .4 ! .7 ! ! -1.1 !
! ! ! .84 ! ! 1.08 ! ! 1.09 ! 1.11 ! ! 1.10 ! ! 1.07 !
2! ! ! .86 ! ! 1.06 ! ! 1.10 ! 1.09 ! ! 1.09 ! ! 1.06 !
! ! ! 2.0 ! ! -1.6 ! ! .4 ! -1.2 ! ! -1.4 ! ! .3 !
! ! .71 ! .87 ! ! 1.33 ! 1.12 ! 1.34 ! 1.12 ! 1.32 ! 1.10 ! 1.08 ! ! 1.27 !
36 ! ! .74 ! .89 ? ! 1.27 ! 1.10 ! 1.31 ! 1.11 ! 1.27 ! 1.09 ! 1.07 ! ! 1.23 !
! ! 4.3 ! 1.6 ! ! -4.5 ! -1.5 ! -2.0 ! -1.3 ! -3.7 ! -1.6 ! -1.6 ! ! -3.2 !
i ! .50 ! ! ! .98 ! 1.06 ! ! 1.09 ! 1.11 ! 1.10 ! ! ! 1.07 ! 1.08 ! 1.00 ! 34 ! .54 ! ! ! .98 ! 1.04 ! ! 1.07 ! 1.07 ! 1.08 ! ! ! 1.05 ! 1.06 ! 1.06 !
! 7.0 ! ! ! .2 ! -1.5 ! ! -1.9 ! -3.7 ! -1.5 ! ! ! -2.3 ' -1.6 ! -1,6 !
! .51 ! .73 ! .87 ! .94 ! 1.01 ! 1.05 ! 1.06 ! 1.08 ! 1.09 ! 1.07 ! 1.05 ! 1.05 ! 1.07 ? 1.11 ! 1.35 !
l 32 ! .54 ! .76 ! .89 ! .96 ! 1.01 ! 1.03 ! 1.04 ! 1.05 ! 1.05 ! 1.04 ! 1.03 ! 1.03 ! 1.05 ! 1.08 ! 1.32 !
! 6.6 ! -3.6 ! 2.4 ! 1.9 ! .5 ! -2.3 ! -1.5 ! -2.7 ! -3.7 ! -2.8 ' -1.8 ' -1.9 ! -2.3 ! -2.7 ! -2.1 !
! 3 5 7 9 11 13 15 17 19 21 23 25 27 29 Figure 3.77 Quad Cities EOC2 Assembly Gamma Scan Comparison I
l l
m m
. 0 3 5 m 1 /
3 D
'2 0 E
/ DT ER m 1 8 R L U U 5
'2 2
S C A L E A m MC
- = 0 X- 0
'2 m N A
C 5Y m S A
- 7. T
'1 I S
M N M E m A G 0N T
- 5. I 2 'l A
E m 8 L C E G L D 7 Y A SE C R mE T 3 E ?. C
'l F V E R O R R U
G E R D mF I O N D 0C I E W 0. D E 'l 1 R . E Z S O ~ I E C M I 5 L A T 1 t I 7. R
'0 C O N
M D A U 0 Q 5 M '0 M 6 2
'0 M
0 0 m . 8' " 8W 8d E 8f 8~ r NM 8k Eb $Ra m t m
I I FIGURE 3.79 COMPARISON OF ASSEMBLY POWERS, SIMULATE VS. HETEROCENEOUS PDQ 3 x 3 ARRAY I 40% Void , 25 GWD/T in Outer 8 Assemblies I K-EFF Central Assembly S DIU LATE PDQ Exposure Void GWD/T % W I .993 1.008 .989 PDQ
.992 1.002 .992 SIMULATE I - . 069 1.008
.602 1.033
.292
.997
% Dif 0.9650 30 0 I 1.002
.599 1.023 1.015 1.002
.523 0.9646
.989 .997 .986 I .992
.299 1.002
.527
.992
.605 I .981
.977
.999
.994
.976
.977
.371 .527 .075
.999 1.121 .988 0.9710 0.9715 25 0
!g .994 1.117 .994 'g .523 .362 .653 . .976 .988 .972 l .977 .994 .977
.083 .658 l .483 I .923
.907
.958
.958
.917
.908
-1.681 .039 .992
.958 1.523 .946 1.0023 1.0024 5 0
.958 1.537 .959
.027 .923 1.346
.917 .946 .912
.908 .959 .908 I .966 1.359 .392 114 I
1 A $e%% i$#.> W+ imies evituiTion TEST TARGET (MT-3) 4 l.0 'ga rag yl} Ha I.I [m HM .
'8 l.25 1.4 '
i.6 l i / < 6~ =
# 4 +4 %
Afh/ 4 777,
#t +kO
<g,#
(.p B' <
%[)> __
TEST TARGET (MT-3) 1.0 5m BE 8
~ y ,7] EM l.l E85 LM VA l.25 IA 1.6 I
4% /4
*:1tV>h/
#'+A>
b? 1
I FIGURE 3.80 COMPARISON OF ASSEMBLY POWERS, SIMULATE VS. HETEROGENEOUS PDQ 3 x 3 ARRAY 40% Void , 25 GWD/T In Outer 8 Assemblies I K-EFF Central Assembly SIMU LATE PDQ Exposure Void i GWD/T I 1.008 1.011
.267 1.006 1.005
.056 1.009 1.011
.223 PDQ SIMULATE
% Dif 1.006 .942 1.006 1.005 .938 1.004 0.9672 0.9675 30 40
- . 059 .396 .195 1.009 1.006 1.009 1.011 1.004 1.010
.218 .197 .069 I .958 .974 .958
.951
.950 .979
.874 .524 .720
.974 1.276 .973 0.9944 0.9943 5 40 I .979
.532 1.280
.325
.979
.643
.958 .973 .957
.951 .979 .951
.704 .651 .628 ;
i . l 115 i l l l
I FIGURE 3.81 CC" PARIS 0N OF ASSEMBLY POWERS, SIMULATE VS. HETEROGENEOUS PDQ I 3 x 3 ARRAY 40% Void , 25 GWD/T In Outer 8 Assemblies K-EFF Central Assembly S IMU LATE PDQ Exposure Void i G79/T % I 1.022 1.028
.565 1.003 1.007
.422 1.026 1.027
.131 PDQ SIMUIATE
% Dif 1.003 .868 1.012 0.96S7 0.9693 30 70 1.007 .868 1.006 414 .018 .579 1.026 1.012 1.029 1.027 1. 006 1.026
.113 .587 .293 1.016 .999 1.020 1.019 1.003 1.019
.261 .360 .055
.999 .907 1.008 0.9722 0.9726 25 70 1.003 .909 1.004
.35 .264 .405 1.020 1.008 1.023 1.019 1.004 1.019
.071 .413 .354 I .989
.966 .964 I __
.983
.306
.992
.836
.984
.521 I .M4
.992
.836 1.095 1.098
.293
.991
.992
.128 0.9889 0.9890 5 70
.989 .991 .992
.984 .992 .984 116
.523 .127 .789
i I FIGURE 3.82 COMPARISON OF ASSE"BLY POWERS, SIMULATE VS. HETEROGENE0US FD0 Radial Plane Typical of Bottom of Core
- 4 - - .
- - -4 1 . -1 -? 14 >
- 6 - - 1 -1 5 g
- - - 3 6 1 -
- - - - -5 1 3 3
- -2 6 4 3' 5 1.5 72 1.414 1.349 1.394 1.300 1.059 .822 .644 420
-1'g g
$ k kh5 2'!Ok 5 Ok 7 9k6 I i i
i i i i 3 i 53 5 i 7 i SIMULATE: K-EFF 1.0280 1.g 70 65 ~g {7 3 I I 9 bc, 3
-4 - 251 1* 1 6$
-{341-6 PDQ: 1.0291 1 5 10 4 6 5 .i 5 ASSEMBLY TYPES EXP VOID CONTROL l ,- I4D ,-
i i i 1 0 0 No 0 0 Yes l 2 6 afl 2 I Key: 117 I
I FIGUP.E 3 83 COMPARISON OF ASSEMBLY POWERS, SIMULATE VS. HETER 0GFNEOUS PD0 Radial Plane Typical of Core Mid-Plane 1 3 1 1 3 1 1 2 1 1 I 2 1 -1' i i i i i i i i i 1 1 2 1 1 2
-1 - - - i 2 1.248 1.205 1.203 1.248 1. 67 1.238 1.128 1.042 .582
'b-g
- '6hh 'lIh l*$fh 5 3 N 2 3 i i
- - i i i -!k I i i 2i0 K-EFF l
- g g
Ug 2g 3 6f SIMULATE: 1.0266 l g
- L - - 3 3
^""'""'
!I -32 ':5J dlli I 3 3 I EXP VOID CONTROL l l -2 3 5f 1 2 0 0 40 0 No Yes 3 0 0 No I KMau I m I
I FIGURE 3.84 I COMPARISON OF ASSEMBLY POWERS, SIMULATE VS. HETEROGENEOUS PD0 Radial Plane Typical of Top of Core I 24 i 2
-1) i, 1
.i 3
i l i:i i i -4 i 4 1 - - - -' . i - >
- -4 l A g tj L
-4 -7 l
z j j - - 3f g g I 2 i 5 i i i i i
- i i
i
- 3 i
908 .8% .929 1.006 1.068 1.123 1.276 1.056 766 1{$hh*$hhl*$hh$h$-)*$N-}dh-1kN 4 2* l 4 i 1 i l'i 2 i 3 i 1 i i
- 1 i V,- E FF l 4 4 1 2 7 su:uuTE: 1.0030 I 3 i 3
- },
1i 2 i 2 i i ASSEMs2 1 m S 3g2{ gig 4g g j EXP VOID CONTROL I 3h 2I -1
$ 2 0 40 Yes 3 0 40 No I Lhm
'I l 119 lI
- w w- -e e- ., + - w g- y a9-g-- *9 gy ~ mv g 4 - -~ g- - y
I TABLE 3.1 Characteristics of Vermont Yankee and Quad Cities PLAtiT VEFM0f1T YANKEE QUAD CITIES 'I .! REACTOR GE GE l
'l RATED THERMAL POWER (MWT) 1593 2511 i
RATED AVERAGE POWER DENSITY (KW/L) 50.96 40.83 NUMBER OF FUEL ASSEMBLIES 368 724
'l CORE LOADING (STU)
~ 70 MTU ~154 4
DATE OF ltilTI AL OPERATION 1971 1972 l FUEL LATTICE 7X7, 8X8 7X7, 8X8 BURNABLE Poison B-SS CURTAINS GD 0 2 3 jl GD 0 23 I I. I . 120 [ i f I-
,-,-+,e--,- .- ,,.-----w--, ,e-w,-.,ww-,v-w,,,,,-m,ev.
I t ll i 11 I Il r
' TABLE 3.2 i ill Operating H ory of Fuel in Vermont Yankee t
j ll < l lll E*: Ass ;tCa t i < (1161 EY:CsU:Es des":I TION OF NEa FUEL r fiuw.EEE C: AVE. EU:'.A ' AssE-ELIEs LATTICE Es: Icu. Poison CO'c ! Tic . 12; ECC 0.0 3u00 358 7x7 2.50 Cu:TAINs Futt 1 t 7x7 2.30 350 2.5% ;LusSEO l 2 3300 7100 40 l l I ! 300 5300 325 Ex8 2.19 33: L: Fctt 3 r
- - P>.es;E3 i 3A 5300 9300 0 -
t, cs e_.. 4 s2,e
, -,5 ;
. ---n .--ce LLCVU 2-ksc Cx.e L.,/= ,J L=s La CCas I
~ !
l c
- 8. Sx5 2.7t SG; 2E3% D:ILLE9 !
5 8100 13500 L i 35 Ex5 2.70 500 213% 11500 C:rt_E l 8900 ' I 6 50 8xS 2.89 7Go 3% l D 0 - - - D*iLLE3 6A 11000 14300 , s 15900 95 8x8 2.83 7G3 3% E:!LLio 7 9500 f I I 121 : ll
TABLE 3.3 f Results of Vermont Cold Critical l Analyses l i I I Exposure Sequence Notches K-e f f ec tive Cyc le ( L'D/ ST) 297.0 331 '3264 .9975 3 4381.8 3A2 3216 .9883 3 4A2 2560 .9923 , 4 8509.9 4B2 2400 .9905 4 10031.2 4B2 3176 .9868 4 12948.9 I 5 5 7794.1 11040.0 SA1 5A2 3456 3456
.9878
.9863 SB2 3262 .9858 5 13067.0 8863.6 6Al 3488 .9868 6
6A2 3166 .9898 6A 10998.1 6B1 3178 .9883 6A 14322.8 7Al 3400 .9907 7 9524.4 7B2 3206 .9902 7 11238.6 7A2 3132 .9877 7 12427.9 I 7 13881.3 15721.8 7B1 7B1 3164 3200
.9879
.9922 7
l average .9894 6
+
._.0029 I
I I I 122 I
I I REFERENCES
- 1. EPRI Contract Number RP710-1.
D. L. Delp, et al. , " FLARE, A Three-Dimensional Boiling Water Reactor I 2. Simulator", GEAP-4598 (1964).
- 3. L. Goldstein, F. Nakache and A. Veras, " Calculation of Fuel-Cycle Burnup I and Power Distribution of Dresden-I Reactor with the TRILUX Fuel Manage =ent Program", Trans. Am. Nuc. Soc. , 10, 300 (1967).
I 4. S. Borrensen, "A Simplified, Coarse Mesh, Three-Dimensional Diffuslen Scheme for Calculating the Gross Power Distribution in a Boiling Water Reactor", Nuclear Science and Engineering, M , 37-43 (1971).
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- 6. A. Ancona, et al., " Nodal Coupling by Response Matrix Principles",
Nuclear Science and Engineering, 64, 405 (1977). K. S. Smith, A. F. Henry and R. A. Loretz, "The Determination of I 7. Homogenized Dif fusion Theory Parameters for Coarse Mesh Nodal Analysis", in 1980 Advances in Reactor Physics and Shielding, Sun Valley, Idaho (September 1980).
- 8. K. Koebke, "A New Approach to Homogenization and Group Condensation",
IAEA Technical Committee Meeting on Homogenization Methods in Reactor Physics, Lugano, Switzerland (November 1978).
- 9. M. Becker, " Incorporation of Spectral Effects into One Group Nodal Simulators", Nuclear Science and Engineering, _59, 3 (March 1976).
- 10. G. Lellouche and B. L. Zolotar, to be published as an EPRI Special Report.
- 11. A. A. Farooq Ansari, " Methods for the Analysis of *d id tg Vater Reactors -
Steady State Core Flow Distribution Code (FIBWR)", L %-1234 (December 1980).
- 12. Letter from Ver=ont Yankee Nuclear Power Corp., to USAEC, " Proposed Change 16", DPR28, Docket 50-271 (November 6,1973).
- 13. R. S. Varga, Patrix Iterative Analysis, Prentice-Hall, Inc., Englewood Cliffs, N. J., p. 73, (1962).
- 14. L. A. Hageman, " Numerical Methods and Techniques Used in the Two-Dimensional Neutron-Dif fusion Program PDQ-5", WAPD-TM-364 (1963).
- 15. L. . A. Hageman and C. J. Pfeifer, "The Utilization of the Neutron Dif fusion Program PDQ-5", WAPD-TM-395 (1965).
I 123 I
I I 16. N. H. Larsen, C. R. Parkos and O. Raza, " Core Design and Operating Data for Cycles 1 and 2 of Quad Cities 1", EPRI-NP-240 (Novesber 1976).
- 17. Martin B. Cutrone and George F. Valby, " Gamma Scan Measurements at Quad Cities Nuclear Power Station Unit 1 Following Cycle 2", EP21-NP-214 (July 1976).
l 18. D. J. Denver, E. E. Pilat and R. J. Cacciapouti, " Application of g Yankee's Reactor Physics Methods to Maine Yankee," YAEC-1115 (0:tober g 1976).
- 19. E. E. Pilat, " Methods for the Analysis of Boiling k'ater Reactor' Lattice Physics", YAEC-1232 (December 1980).
I I I I
- I I .
I I I I I 124
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