ML20151M597

Validation of Fuel Accountability Nodal,3 Dimensional Model for Fort St Vrain Fuel Accountability Calculations

ML20151M597
Person / Time
Site:	Fort Saint Vrain
Issue date:	07/06/1988
From:	Malakhof V PUBLIC SERVICE CO. OF COLORADO
To:
Shared Package
ML20151M591	List: ML20151M586 ML20151M597
References
TAC-69028, NUDOCS 8808050252
Download: ML20151M597 (156)

Text

i o,,,,m./*,,**'6 GA Techn:logi s inc ISSUE

SUMMARY

TITLE Validation of FAN 3D Zbdel for FSV Fuel OR&D APPROVAL LEVEL 2

Accountability Calculations 00V&S O DESIGN DISCIPLINE SYSTEM 000. TYPE PROJECT DOCUMENT NO. ISSUE NO./LTR.

N 18 RGE 1900 909436 A r QUAllTY ASSURANCE LEVEL SAFETY CLASSIFICATION SEISMIC CATEGORY ELECTRICAL CLASSIFICATION

,G OAL-I FSV-I FSV-I N/A Q. . , APPROVAL ISSUE PREPARED DATE FUNDING APPLICABLE DESCRIPTION /

BY ENGINEERING QA Q@I PROJECT PROJECT CW8S NO.

G .- vwuu,py N/C JAN 18 $69 . per .hp G. ConnorE V,.Malakhof Initial Release K(\'h.Yys s

D M ha L ma..L ' ~ ' '

J.Alberstei n(2970889 i

$ aathew

-sv-pi

[.gL k- --.b

$ thh3 4

A R 0 6 1908 v. Malakhof Release Basis:

h cm/n

_ CN-005763 z

/

I CONTINUE ON GA FORM 14851 N EXT IN O ENTU RED

, ~ - -

DOCUMENTS

• See List of Effective Pages.

905982 30N-00STh LLL 7Y  !

VERIFY N i \"

~~

u h,> /

G A PROPRIETARY INFORMATION THIS DOCUMENT IS THE PROPERTY OF GA TECHNOLOGIES INC. ANY TRANSMITTAL OF THIS DOCUMENT OUTSIDE GAWILL BE IN CONFIDENCE. EXCEPT WITH THE WRITTEN CONSENT OF GA,(1) THIS DOCUMENT MAY NOT BE COP!ED IN WHOLE OR IN PART AND WILL BE RETURNED UPON REQUEST OR WHEN NO LONGER NEEDED BY RECIPIENT AND (2)INFORMATION CONTAINED HEREIN MAY NOT BE COMMUNICATED TO OTHERS AND MAY BE USED BY RECIPIENT ONLY FOR THE PURPOSE FOR WHICH IT WAS TRANSMITTED.

[

NO GA PROPRIETARY INFORMATION 8808050252 800722 PDR ADOCK 05000267 PAGE 1 O r_*

P PNU )

909436 A LIST OF EFFECTIVE PAGES

.g Page Number Page Count Revision Issue Sununary 1 A i 1 A 11 through iv 3 N/C 1-1 throur,h 1-2 2 N/C l 1-3 1 A l 2-1 through 2-4 4 N/C 3-1 through 3-6 6 N/C 4-1 through 4-17 17 N/C 5-1 through 5-57 57 N/C 6-1 through 6-4 4 N/C 7-1 through 7-4 4' N/C 8-1 through 8-3 3 N/C l Appendix A-1 to A-17 17 N/C

'& Appendix B-1 to B-28 28 N/C Appendix C-1 to C-7 7 N/C Microfiche 179 N/C

,- Computer output -

MUN0Z 22 N/C ST 6460 20 N/C ST 6461 20 N/C ST 9860 12 N/C ST 3799 20 N/C MATHEWS 29 N/C Total Pages 457 NOTE: Microfiche and computer output are not distributed.

I I i f

i

)

Date: July 6, 1988

?

t w' From: Configuration Management To: See Document Distribution List

Subject:

DOCUMENT REVISION

SUMMARY

UPDATE Update Document Number 909436- N/C ,

. Validation of FAN 3D 4xlel for FSV Fuel Accountability Calculations 909436/A

, to

. as indicated below with the attached.

Remove Add Page(s) Rev. Page(s) Rev.

1 N/C 1 A i N/C i A 1-3 N/C 1-3 A I

i i 4 l

909436 A' X-MP/48 and on the IBM-3090 used by PSC. Section 5 discusses the DIF3D calculations of the FSV fuel accountability for 170.4 to 294.5 effective e, full-power days (EFPD) of Cycle 3. This time period was chosen because of the relatively good core-outlet temperature measurements toward the f c. end of the period and because 3-D GATT calculations had previously been done for this time period, which could be used for comparison with the DIF3D results. Section 6 summarizes the 3-D DIF3D fuel accountability calculations for Cycle 4. Also included are extc.nsive documentation control (Section 7) and references (Section 8).

The main objective of this validation effort was to allow the FSV fuel accountability calculations to be done in the future with the FAN 3D model, i.e., to proceed with Cycle 4 burnup without the recalculation of burnup from the beginning of the initial cycle. A minimum of six month of Cycle 4 power history will be recalculated with the FAN 3D model e- and compared with fuel accountability results obtained with the GATT model to ensure the consistency of results obtained with FAN 3D. This

.- comparison will be conducted prior ta the use of FAN 3D for fuel account-ability calculations in Cycle 4.

o 4

1-3

i-909436 N/C CONTENTS

1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

2. CONCLUSIONS . . . . . . . . . - . . . . . . . . . . . . . . . . 2-1

3. NODAL METHODOLOGY . . . . . . . . . . . . . . . . . . . . . . . 3-1

4. BENCHMARK PROBLEM ANALYSIS . . . . . . . . . . . . . . . . . . 4-1 4.1. DIF3D Validation for LMFBRs . . . . . . . . . . . . . . . 4-1 4.2. ORNL Validation of DIF3D for HTGRs . . . . . . . . . . . 4-3 4 3. Small HTGR Test Problem . . . . . . . . . . . . . . . . . 4-5 4.3.1. Description of Test Problem . . . . . . . . . . . 4-5 4.3.2. Eigenvalue Results . . . . . . . . . . . . . . . 4-6 4.3.3. Radial Power Distribution Results . . . . . . . . 4-10 4.4. Validation of CRAY Version of DIF3D . . . . . . . . . . . 4-13 4.4.1. DIF3D Conversion to CRAY . . . . . . . . . . . . 4-13 4.4.2. Validation Results . . . . . . . . . . . . . . . 4-14 4.5. Validation of IBM Version of DIF3D . . . . . . . . . . . 4-17

5. VALIDATION OF FSV MODEL . . . . . . . . . . . . . . . . . . . . 5-1 5.1. FSV Cycle 3 Burnup . . . . . . . . . . . . . . . . . . . 5-1 5.2. Calculational Sequence . . . . . . . . . . . . . . . . . 5-2 5.2.1. 2-D Calculations . . . . . . . . . . . . . . . . 5-2 5.2.2. 3-D Calculations . . . . . . . . . . . . . . . . 5-8 5.2.3. DIF3D Model . . . . . . . . . . . . . . . . . . . 5-13 5.2.4. Differences Between DIF3D and GATT Calculations .. . . . . . . . . . . . . . . . . 5-16 5.3. Reactivity Comparison . . . . . . . . . . . . . . . . . . 5-20 5.3.1. 2-D Reactivity Comparison . . . . . . . . . . . . 5-20 5.3.2. 3-D Reactivity Comparison . . . . . . . . . . . . 5-22

• 5.4. Radial Peaking Factor Comparison . . . . . . . . . . . . 5-22

. 5.4.1. 2-D RPF Comparison . . . . . . . . . . . . . . . 5-22

. 5.4.2. 3-D RPF Comparison . . . . . . . . . . . . . . . 5-30 5.5. Axial Peaking Factor Comparison . . . . . . . . . . . . . 5-39 5.6. Fuel Accountability Comparison . . . . . . . . . . . . . 5-44 11

909436 N/C

6. 3-D BURNUP FOR CYCLE 4 . . . . . . . . . . . . . . . . . . . . 6-1

7. DOCUMENTATION CONTROL . . . . . . . . . . . . . . . . . . . . . 7-1 7.1. Code Versions . . . . . . . . . . . . . . . . . . . . . . 7-1 7.2. Data Storage . . . . . . . . . . . . . . . . . . . . . . 7-1

8. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1 APPENDIX A TWO-DIMENSIONAL RADIAL PEAKING FACTOR COMPARISONS AT TIME POINTS 640 AND 650 . . . . . . . . . . . . . . A-1 APPENDIX B: THREE-DIMENSIONAL RADIAL PEAKING FACTOR COMPARISONS FOR CYCLE 3 . . . . . . . . . . . . . . . . . . . . . B-1 APPENDIX C: THREE-DIMENSIONAL RADIAL PEAKING FACTOR COMPARIS0NS FOR CYCLE 4 . . . . . . . . . . . . . . . . . . . . . C-1 FIGURES 4-1. Core layout for HTGR test problem . . . . . . . . . . . . . 4-7 5-1. GA sequence for 3-D calculations with DIF3D . . . . . . . . 5-9 5-2. PSC sequence for 3-D calculations with DIF3D . . . . . . . . 5-12 5-3. Fort St. Vrain core layout . . . . . . . . . . . . . . . . 5-14 5-4. 3-D geometry in nodal DIF3D for Fort St. Vrain . . . . . . . 5-15 5-5. 3-D models to determine effect of exterior low-density region . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-18 5-6. Effect of exterior region removal . . . . . . . . . . . . . 5-19 5-7. Extrapolation of 2-D results to zero triangle size . . . . . 5-21 5-8. k-eff calculated by 3-D codes . . . . . . . . . . . . . . . 5-24 5-9. Standard deviation between GATT and DIF3D RPFs . . . . . . . 5-31 5-10. Standard deviation between calculated and messured RPFs. . . 5-34 5-11.  % Difference between GATT and DIF3D RPFs . . . . . . . . . 5-35 5-12.  % Difference between calculated and measured RPFs. . . . . . 5-37 <

5-13. FSV Region k-infinite . . . . . . . . . . . . . . . . . . . 5-38 TABLES 4-1. Calculations of the SNR-300 benchmark LMFBR . . . . . . . . 4-2 l

4-2. ORNL calculations of the HTGR benchmark . . . . . . . . . . 4-4 4-3. Comparison of eigenvalues for a small fully rodded HTGR core . . . . . . . . . . . . . . . . . . . . . . . . . 4-8 I

lii l

l_

909436 N/C 4-4. Radial powers for a small fully rodded HTGR core . . . . . . 4-11 4-5. Eigenvalues calculated by a nodal DIF3D using a

• preliminary 3-D model of FS"r . . . . . . . . . . . . . . . . 4-15 4-6. Eigenvalues calculated for ANL test problems

. . . . . . . . 4-16 4 5-1. FSV power history used in Cycle 3 fuel accountability

. GAUGE calculations . . . . . . . . . . . . . . . . . . . . . 5-3 5-2. FSV control rod withdrawal sequence for Cycle 3 . . . . . . 5-4 l-5-3. Power history used for 3-D calculations in Cycle 3 . . . . . 5-5 l 5-4. Cold / hot 2-D calculations in seven groups . . . . . . . . . 5-7

! 5-5. 3-D model comparison in Cycle 4 . . . . . . . . . . . . . . 5-17 5-6. 3-D calculations for FSV Cycle 3 . . . . . . .. . . . . . . 5-23 5-7. Sunnary of 2-D RPF comparisons . . . . . . . . . . . . . . . 5-27 5-8. Sumnary of 3-D RPF comparison . . .. . . . . . . . . . . . 5-32 5-9. GATT axial peaking factors at 3/21 . . . . . . . . . . . . . 5-40 5-10. DIF3D axial peaking factors at 3/21 . . . . . . . . . . . . 5-41

,, 5-11. Power fraction in top half of core . . . . . . . . . . . . . 5-42 5-12. Axial power factors in bottom layer . . . . . . . . . . . . 5-43 5-13. GATT fractional absorptions . . . . . . . . . . . . . . . . 5-45 5-14._ DIF3D fractional absorptions . . . . . . . . . . . . . . . . 5-46 5-15. GATT core loadings . . . . . . . . . . . . . . . . . . . . . 5-47 5-16. DIF3D Core loadings . . . . . . . . . . . . . . . . . . . . 5-48 5-17. GATT fissile particle burnup at 3/32 . . . . . . . . . . . . 5-49 l 5-18. DIF3D fissile particle burnup at 3/32 . . . . . . . . . . . 5-50 5-19. GATT fertile particle burnup at 3/32 . . . . . . . . . . . . 5-51 5-20. DIF3D fertile particle burnup at 3/32 . . . . . . . . . . . 5-52 5-21. Radial burnup distribution . . . . . . . . . . . . . . . . 5-53 5-22. Axial burnup distribution . . . . . . . . . . . . . . . . . 5-54 5-23. Axial burnup in region 1, column 4 . . . . . . . . . . . . . 5-55 6-1. Power history for 3-D Cycle 4 calculations . . . . . . . . . 6-2 6-2. Control rod withdrawal sequence for Cycle 4 . . . . . . . . 6-2

, 6-3. GATT/DIF3D comparison for Cycle 4 . . . . . . . . . . . . . 6-3 iv

909436 N/C

1. INTRODUCTION The NRC requires the reporting of nuclide densities for each fuel element in the Fort St. Vrain (FSV) core as burnup progresses. As a result, three-dimensional (3-D) calculations have been done in the past by GA Technologies Inc. on the UNIVAC computer using the 3-D diffusion theory GATT code. To improve the efficiency of 3-D calculations, Public Service Company of Colorado (PSC) and GA sought to validate the DIF3D code for use by GA and PSC in the fuel accountability calculations (the FAN 3D program) for FSV. The DIF3D code solves two- and three-dimensional diffusion theory problems using finite-difference and nodal methods.

Relative to GATT, DIF3D is better documented (Ref. 8 and 21), and the program is easier to modify. DIF3D in the nodal option is much faster and less expensive than GATT. Unlike GATT, the DIF3D code is opera-tional, or could be easily made so, on a number of advanced computers other than UNIVAC.

The DIF3D code was developed primarily for fast reactor applications and has been used extensively at ANL and elsewhere as a tool for the design and analysis of homogeneous and heterogeneous LMFBR systems.

Because of its cost and accuracy benefits, it has also been used exten-sively for design and fuel cycle analysis of water-cooled reactors.

The standard finite difference option in the DIF3D code solves the multigroup diffusion theory equation in one , two , or three-dimensional geometries (rectangular, cylindrical, triangular, etc.). The current

- version of DIF3D also contains both rectangular and hexagonal nodal tech-niques as options, so users may elect the finite difference or nodal option with relative ease. Thess features, together with its reported advantages in cost and accuracy, make DIF3D very attractive for HTGR use.

1-1

909436 N/C In a recent study (Ref. 7) of applying hexagonel nodal methods to HTGR analysis, the following conclusion was reached:

"The state-of-the-art in neutronics capability for LWR and LMFBR physics analyses is moving away from standard finite difference methods to the more computationa31y efficient nodal techniques. The overall goal of this study was to address the potential for adapting nodal methods for HTGR applications, with the incentive of reducing the tremendous cost associated with large three-dimensional HTGR neutronics calculations.

Because of its availability and previously reported suc-cess for LMFBR applications, the DIF3D nodal option was chosen for this evaluation. The nodal option of DIF3D showed nearly an order of magnitude cost advantage over ORNL's current capa-bilities for performing largo HTGR hex-Z computations. In addition, there was an associated increase in accuracy in the global eigenvalue as well ar, the regionwise power distribu-tion. The efficiency and accuracy of this nodal method appears to apply to HTGRs as well as LMFBRs, and, therefore, further efforts should be directed t<> ward the utilization of this available technology for benefit within the HTGR program."

The present study was performed as an additional effort to vali-date nodal methodologies to HTGR analysis in 'eneral, g and to FSV in particular.

Section 2 in this report summarizes the conclusions of this study.

Section 3 discusses the solution technique used in the DIF3D nodal meth-odology. Section 4 reviews previous efforts to validate the DIF3D code for othat reactor types, and the DIF3D results for a small HTGR test problem. Alao discussed are the actions that were necessary to obtain working DIF3D versions on the San Diego Supercomputer Center (SDSC) CRAY 1-2

909436 N/C

2. CONCLUSIONS-The main conclusions of this study, based on a comparison of the three-dimensional nodal DIF3D results versus GATT results over the'170.4 to 294.5 EFPD burnup period of FSV Cycle 3, are as follows:

1. k-off values calculated by the 3-D codes are very close to each other (Ak ( 0.002). The GATT k-eff was the same as, or highor than, the nodal DIF3D k-eff. The nodal DIF3D code calculated the k-off to be closer to criticality (k = 1.0) than the GATT code during the 124 EFFD burnup (Fig. 5-8).

2. The radial peaking factors (RPFs) calculated by th'e 3-D GATT

! and nodal DIF3D codes - (Appendix B) were generally within about 7% of each other at the beginning of the burnup period. The differences between the GATT and DIF3D RPFs decreased with burnup until, at the end of the burnup period, they were generally within about 3.5% of each other (Fig. 5-9, Appendix B-14).

3. DIF3D calculated RPFs were generally about 2% closer to the RPFs calculated from the core-outlet gas temperature, than were the GATT calculated RPFs (Fig. 5-10).

4. The radial power distribution calculated by DIF3D 1.s shifted

toward the center of the core, and sway from the core radial

- reflector interface, relative to the radial power distribu-tion calculated by GATT (Appendix B-14). For regions 20 through 37, which are the regions next to the radial reflec-tor, the DIF3D RPFs are generally about 3.5% less than the GATT RPFs (Fig. 5-11). This effect is apparently due to the 2-1

- - _ _. . _ _ _ _ _ _ , _ _ __ _ _ . _ . _ __ __. . _ , _ _ . - _ . _ _ _ . . ____m

909436 N/C mesh corner versus mesh center diffusion approximation used in GATT and DIF3D, respectively. The tilting of the power toward the core center results in lower neutron leakage losses in the DIF3D model, as compared with GATT.

L

5. DIF3D calculates a more accurate radial power distribution than GATT (Appendix B-21 and B-28). For regions 20 through 37, the DIF3D RPFs are generally about 4% closer to the RPFs calculated from the core-outlet gas temperature, than vere the GATT calculated RPFs (Fig. 5-12).

6. The largest difference between DIF3D and GATT RPFs were in the northwest sector of the core (Appendix B-2), where the core region k-infinities were the largest (Fig. 5-13).

7. The largest difference between the axial peaking factors cal-culated by DIF3D and GATT was only 0 or 3% (Tables 5-9 and 5-10).

8. The fractional absorptions are generally within 1% between the DIF3D and GATT calculations, including the fractional absorptions for the control rods (Tables 5-13 and 5-14). This means that the control rod effective shielding factors used in the GATT calculations are also valid for the DIF3D calcula-tions without any modifications. ,

9. Core loadings at the end of the 124 EFPD burnup are generally within 1% between the GATT and DIF3D calculations (Tables 5-15 and 5-16).

10. The incremental fuel element burnups over the 124 EFPD period may differ by up to 10% to 13% (Tables 5-21 and 5-22) as a result of radial, axial, and standard column / control column 2-2

m. . . . . . ..

r_

L l_

909436 N/C power differences between the GATT and nodal DIF3D calcula-tions. However, most incremental block burnups calculated by GATT and DIF3D are within about 5% of each other due to the l

good agreement between the calculated powers for most fuel .

elements in the core. Where the DIF3D fuel element burnups differ from the GATT burnups, the DIF3D burnups are usually closer to the actual values because DIF3D power distributions-are closer to the measured values (points 3 and 5-above).

The above conclusions from the GATT/DIF3D comparisons in Cycle 3 I

were also confirmed by GATT and DIF3D burnup calculation. frem 4.9_to 24.9 ETPD in Cycle 4 (Section 6).

Two-dimensional calculations in Cycle 3 using the GAUGE, BUGTRI, and DIF3D codes also confirmed the above conclusions regarding the accu-racy of k-eff and radial peaking factors calculated using the nodal option in DIF3D. The other main conclusions, based on these 2-D calcu-lations, are as follows:

-1. The cold-to-hot k-off discrepancy noticed for previous GAUGE calculations of FSV is mostly due to the use of a small number of mesh points in the finite difference approximation to the diffusion equation (Section 5.3.1). The nodal calculations do not show such reactivity discrepancy.

2. Relative to the reference BUGTRI power distribution, the nodal DIF3D is a better calculation than the 6 triangle / hex DIF3D, but not as good as the 24 triangle / hex DIF3D (Appendices A-8, A-9, r. 3 10).

3. In general. the GAUGE RPFs and nodal DIF3D RPFs are equally different, though in opposite directions, from the reference BUGTRI RPFs (Appendices A-7 and A-8). This is apparently due to the mesh corner versus mesh center diffusion approximation 2-3

-l 909436 N/C l used in the GAUGE and DIF2D codes, respectively. Both of these codes are therefore equally acceptable for HTGR ,

application.

~~

4. The nodal DIF3D RPFs are generally in better agrcament with the RPFs calculated from the measured core-outlet temperatures than the GAUGE RPFs (Appendices A-13 and A-14).

• Therefore, to obtain equally or more accurate calculational results, the DIF3D code in the nodal option could be used for two- and three-dimensional fuel accountability calculations for the Fort St.

Vrain reactor, as well as for other HTGR analysis. This is also econom-ically desirable because of the much faster running times for DIF3D.

For example, a typical 3-D static calculation of FSV takes about 60 min on the GA UNIVAC-1100/82 computer (about $800) with the GATT code, whereas it takes only 4 min on the SDSC CRAY computer (about $120) with the DIFSD code in the nodal option.

These conclusions confirm a previous study (Ref. 7) of the applica-tion of nodal methods to HTGR analysis.

G e

O 2-4

909436 N/C

3. NODAL METHODOLOGY There is a need for calculational methods suitable for cost-effective High-Temperature Gas-Cooled Reactor (HTGR) core neutronics analysis. This need translates into a requirement for accurate com-putations of the neutron multiplication factor.and the power distr'bu-tion in an HTGR core, together with fast execution times. Standard finite difference methods, although they can be made accurate by increasing the number of mesh points, do not serve this purpose, as the cost in terms of computer time is unacceptably high for large caree-dimensional (3-D) problems. Recent developments (Refs. 1 through 6) in the field of nodal or coarse-mesh techniques indicated that a method of this type may be suitable for HTGR core calculations.

A rsview of the subject by John White of the University of Lowell (Ref. 7) indicated that the hexagonal geometry nodal option in the DIF3D code (Ref. S) would indeed be useful for HTGR core calculations. c. sum-mary of nodal methodology based upon White's review follows.

Early nodal techniques were developed largely on an intuitive basis. They relied heavily on empirical "coupling parameters" to relate the nodal leakages or surface currents to the node-averaged fluxes.

These coupling coefficients (or transfer probabilities) in many cases were dertvr.3 from auxiliary fine-mesh calculations or calculated inter-nally using response matrix techniques. The early methods were useful, but also limit ad in that good results could only be expected for sets of similar calculations, where initial adjustments of free parameters were required to benchmark the base results to more accurate fine-mesh calcu-lations. Many nodal codes of this type vere developed (e.g., FLARE (Ref. 9), TRILUX (Ref. 10), PRESTO (Ref. 11), ROCS (Ref. 12), and dIMULATE (Ref. 13)) and extensively used for LWR reload design.

3-1

. . ~ -

909435 N/C Recent nodal methods are distinguished from earlier developments in O

that they are based upon rigorous mathematical formulations from which Inter-node coupling relationships using higher-order approximations to the diffusion equation can be derived. These more recent techniques are formal coarse-mesh approximations that, in the limit of zero node size, can be expected to converge to the exact solution of the diffusion equation.

The one major development that brought nodal methods into the modern era is the so-callad "transverse integration" technique (Refs. 2 and 18). Simple integration of the diffusion equation over the node volume results in a node balance equation that contains surface-averaged leakages (net currents) and the node-averaged flux. Thus, the formal solution of the node balance equations requires additional relationships between the surface leakages and nedal fluxes in adjacent nodes.

Instead of providing dircen coupling relationships in all the directions in a multidimensional model, the transverse integration tech-nique first involves the spatial integration of the n-dimensional diffu-sion equation over the n-1 directions transverse to each coordinate direction. The resulting coupled set of n ordinary differential equa-tions is then solved using techniques appropriate for the numerical evaluation of a 1-D inhomogeneous diffusion equation. The inhomogeneous source term contains the f amiliar fission and inscatter sources as well as the transverse 14akage terms, and it is this latter component that couples the n 1-D diffusion-like equations.

The coupling relationships for the partially integrated node fluxes and surface currents (for the 1-D problem) and an ap'roximation for the

t. ansverse leakage terms can be obtained using several techniques. It is the choice of technique here that distinguishes the various modern nodal methods for Cartesian geometry. These technicues are sometimes' classified ass (1) polynomial methoda (e.g., NEM (Refs. 14 and 15) or NODLEG (Ref. 16) methods) where the 1-D partially integrated fluxes and 3-2

909436 N/C transverse leakages are approximated by polynomials, or (2) analytic

, methods (e.g., QUANDRY (Ref. 17) or AN2D (Ref. 18) methods), where only the transverse leakage term is approximated by some low-order polynomial and then the resultant 1-D inhomogeneous equation is solved analyti-cally. All these modern or transverse methods have been shown to be very accurate and computationally efficient for nodes the size of LWR fuel assemblies (in the plane), and none of the methods seem to be clearly superior (see Table I in Ref. 2). However, the critical feature of this method is the accuracy of the representation for the transverse leakage profile, and a quadratic approximation which extends over three adjacent nodes seems to be adequate for this purpose.

Hexagonal geometry nodal methods directly analogous to the trans-verse or modern methods for Cartesian geometry have also been developed.

., Here the n-dimensional diffusion equation is partially integrated such that n 1-D diffusion-like equations result. The partially integrated

,. fluxes along each direction are coupled through the transverse leakage terms that are treated as inhomogeneous sources in the 1-D expressions.

At least two researchers, R. D. Lawrence (Ref. 8) at ANL and T. Duracz (Ref. 19) at the Institute of Nuclear Research in Poland, have worked through the complexity of extending this t ransverse integration tech-nique to hexagonal-shaped nodas. The result of L2wrence's efforts is the nodal option within DIF3D, and Duracz's approach, which is very similar to that in DIF3D, is a direct extension of the Nodal Expansion Method (NEM) (Refs. 14,15)

The main difficulty in the extension of the transverse integration i

technique to hexagonal geometry is the introduction of additional terms i in the partially integrated diffusion equation that are not directly

( ,

related to the transverse leakage. In particular, because of the vari-l.

able limits of integration, discontinuities result when deriving expan-sions for the partially integrated currents (from the use of Leibnitz's rule for differentiating an integral with variable limits). These dis-continuities also lead to terms containing a Dirac delta function when 3-3

909436 N/C the leakage term of the form d/dx (Jgx (x)] is evaluated. This discos.-

, tinuous behavior complicates the solution of the partially integrated 1-D diffusion equation.

A way to treat this phenomenon is to expand the flux in a series of polynomial functions that provide an approxirttion to the first deriva-tive discontinuity. In particular, DIF3D uses a linear combination of four polynomials, and the third one, although a continuous function of e = x/h, has a discontinuous first derivative at a = 0, where 10 1 3 f 3(x) = 73 62 3 lEl + gg ,

and

- 20 1 f 3(x) = 77 e 7 .

Expansion functions of this form have the desired functional dependence and, therefore, can be effectively utilzied to approximate the discon-tinuous behavior of the current and leakage that result from the trans-verse integration process.

The DIF3D nodal methodology has, therefore, overcome the difficulty associated with the discontinuous transverse integration terms by choos-ing expansion functions that exhibit similar beh:vior. The intra-node polynomial expansions are used along with continuity of flux and current conditions at the node boundaries to develop a consistent inhomogeneous ,

response matrix representation. The response matrix equations are solved by using a conventional fission source iteration scheme. See Refs. 8, 20, and 21 for more details about the DIF3D code.

i

, Benchmark comparisons using the noda3 option within DIF3D have verified the accuracy and efficiency of the technique for the analysis of hexagonal 'MFBR and HTGR cores. Both small and large LMFBR models 3-4

909436 N/C have been compared, and the conclusions were similar. For the most part, the 1-node-per-assembly nodal option is more accurate in the calculation of power distributions than a 6 points / hex mesh centered, finite differe.ce (mefd) case but less than the 24 points / hex mcfd o,

model. As indicated in Ref. 8, CPU times are roughly 2 times smaller in 2-D and 8-10 times sm.11er in 3-D for the nodal option relative to the finite difference option in DIF3D. These LMFBR results were also duplicated in John White's study (Ref. 7). The important point is that increased efficiency is coupled with increased accuracy relative to the 6 points / hex mcfd case. Thus the DIF3D nodal option has been shown to be an accurate and efficient alternative to the mesh centered, finite difference approach and, at ANL, the nodal technique has become the standard design tool for LMFBR physics analysis. The success of the method for LMFBR design is wnat prompted the interest in benchmarking DIF3D for potential HTGR applications.

White (Ref. 7) found that the hexagonal geometry nodal option in the DIF3D code was more accurate and three to four times more efficient than the 6 points / hex mcfd option for certain two- and three-dimensional HTGR test problems.

The standard GA codes, however, use 7 points / hex mesh-edge, finite difference approxications in hexagonal geometry (e.g. , GAUGE (Ref. 22) and GATT (Ref. 23)]. Because the mesh-edge (same as mesh-corner) finita difference (mefd) approximation was thought to be more accurate than mesh-centered, finite difference (mefd) approximations in hexagonal geometry (Ref. 24) and the GA codes are optimized for HTGR calculations, l

it was not clear that the DIF3D hexagonal geometry nodal vption would show such a clear superiority over the 7 points / hex mefd GA codes, GAUGE l

and GATT.

1 l

The results of this work show that the DIF3D hexagonal geometry nodal option is both more accurate and cheaper than the GAUGE and GATT codes for FSV HTGR reactor esiculations. The cost reduction is partly l

3-5

. .._ .- .- =

909436 N/C due to the use of different computers, a CRAY-X-MP/48 for DIF3D and an

, older UNIVAC-1100/82 for GAUGE and GATT. A vectorized version of the GATT code might wcil run at about the same speed as DIF3D on the-ORAY-X-MP/48. However, conversion of the GATT code for operation on the CRAY-X-MP/48 was judged to be prohibitively expensive.

9 9

4 9

3-6

909436 N/C

4. BENCEMARK PROBLEM ANALYSIS 4.1. DIF3D VALIDATION FOR LMFBRs Typical of previous DIF3D validation efforts for LMFBR designs are the calculations in Table 4-1 taken from Refs. 7 and 8. The SNR benchmark problem in Table 4-1 is a four-group model of a 300 MW(e) homogeneous-core LMFBR. The model consists of a two-zone core sur-rounded by radial and axial blankets. The height of the active core is 95 cm, and each axial blanket is 40 cm thick. A total of 11 rings of hexagons (including the central hexagon) are included in the model, with a lattice p ch of 11.2003 cm. Vacuum boundary conditions are imposed on the out' soundaries. The full-core model includes a total of 18 control , with 6 of these rods located at the core-upper axial

~

blanket interface, and the remaining 12 rods inserted to the core mid-plane. The ANL calculations used a model without reflectors, but the ORNL model included large sodium reflectors to permit intercomparison between the ORNL DIF3D and VENTURE calculations, which had different requirements for the outer radial boundaries. The VENTURE code was included in the ORNL comparisons, since this code is the primary tool for physics analyses at ORNL. The reflector differences in the ANL and ORNL models means that the ANL results cannot be directly compared with the ORNL results.

The ANL k-eff results in Table 4-1, and the power distribution comi.arisons in Ref. 8, indicate that the nodal DIF3D calculations are l better than the 6 triangles / hex finite difference DIF3D calculations, 1

but not as good as the 24 triangles / hex finite difference DIF3D calcu-1ations, in both two and three dimensions. The ORNL results confirm this conclusion, and also confirm that the finite difference DIF3D and VENTURE calculations give very close to the same result, as they should, l

l 4-1

a.

4 TABLE 4-1 CALCULATIONS OF TLT ONR-300 BENCHMARK LMFBR 2

ANL Results ORNL Results Axial Dimensions Code Method Per Hex Nodes k-eff Ak k-eff- Ak 2 VENTURE Finite Difference 6 1.13244. 0.00323 DIF3D Finite Difference 6 1.12728 0.00353 1.13241 0.00320 24 1.12475 0.00100 1.13001 0.00080 m 1.12375(a) --

1.12921(a) __

DIF3D Nodal 1 node / hex 1.12529 0.00154 1.13037 0.00116 I 3 VENTURE Finite Difference 6 36 1.01792 _

7 DIF3D Finite Difference 6 18 1.01505 0.00516 N

6 36 1.01280 0.00291 1.01800

, 6 m 1.01205 0.00216

24 18 1.01342 0.00353

24 36 1.01118 0.00129

, 24 a 1 01043 0.00054

]

1. # 1.00939(a) __

DIF3D Nodal 1 node / hex 8 1.01150 0.00161 1.01665 1 node / hex 18 1.01125 0.00136  :

1 node / hex e 1.01120 0.00131-(a) Reference values obtained by Richardson extrapolation.

~

E o

1

l l

909436 N/C 1 since both codes use a mesh-center approximation to the diffusion equa-  !

tion. Thus, it appears that the DIF3D nodal scheme offers both accuracy

. and efficiency relative to the standard finite difference tools commonly in use tor LMFBR physics analyses.

The conclusions of this brief analysis of the SNR-300 benchmark are consistent with previously reported results for large LMFBRs (Ref. 30).

Thus, for LMFBR problems, the nodal option in DIF3D represents a signif-icant improvement over ORNL's current capabilities within VENTURE. For a large class of problems, the DIF3D nodal option can offer a cost sav-ings of about a factor of 3 to 4 for 2-D hexagonal problems and reduc-tions for 3-D hex-Z computations of about 10 to 12 are not unreasonable.

An additional benefit of the nodal method is that it is also more accu-rate than the standard six points per hexagon finite difference scheme.

4.2. ORNL VALIDATION OF DIF3D FOP HTGRs

~~

Table 4-2 lists a fairly extensire set of computations performed by ORNL on the HTGR benchmark (Ref. 27). The k-eff values and power distributions (Ref. 7) compare exactly between the finite difference VENTURE and DIF3D calculations in both two and three dimensions. The nodal DIF3D calculations are as good or better than the 6 triangles / hex finite difference calculation of k-eff, and the nodal DIF3D power dis-tribution is nearly as accurate as a 24 triangles / hex finite difference calculation (Ref. 7).

In the 2-D LMFBR problem, the nodal technique was faster by almost a factor of two, but for this HTGR cc figuration, there is essentially no difference in the computational cost of the one-node-per-assembly l - nodal option versus the 6 triangles / hex finite difference model. Thus,

!- for essentially the same cost (using DIF3D), it appears that the nodal method is more accurate than the 6 triangles / hex finite difference model not only for the global eigenvalue (Table 4-2) but also for the l

l assembly-averaged powers. With accuracy as a base, the nodal method l

4-3

TABLE 4-2 ORNL CALCULATIONS OF THE HTGR BENCHMARK Diffusion Triangles Axial Dimensions Code Approximation Per Hex- Nodes k-eff Ak 2 VENTURE Mesh Center F.D. 6 1.12028 0.00168 24 1.11891 0.00031 54 1.11860 0.0000G DIF3D Mesh Center F.D. 6 1.12028 0.00168 24 1.11891 0.00031 54 1.11860(a) .__

DIF3D Nodal 1 node /her 1.11857 -0.00003 7

3 V7NTURE Mesh Center F.D. 6 8 1.09069 0.00036 6 16 1.09063 0.00030 DIF3D Mesh Center F.D. 6 8 1.09069 0.00036 6 16 1.09063 0.00030 6 32 1.09137 0.00104 24 64 1.09033(a) __

DIF3D Nodal 1 node / hex 8 1.08992 -0.00041 1 node / hex 16 1.09028 -0.00005 1 node / hex 32 1.09032 -0.00001 (a)Used for reference values.

F.D. = Finite Difference.

E o

909436 N/C shows a cost savings of about 3 to 4 compared to the 24 triangles / hex case. Thus, while not as impressive as for the LMFBR benchmark compari-sons the 2-D nodal option in DIF3D still has some advantages over the standard finite difference method for HTGR computations.

Some difficulty was encountered in comparing the 3-D k-eff results for the nodal and finite difference cases. As seen in Table 4-2, the 3-D eigenvalue is not a well-behaved function of the mesh spacing. It is likely that there is some cancellation of errors involved that gives a coarse-mesh result that is reasonably close to the correct fine-mesh solution. In the coarse mesh model, there are eight axial mesh points over 634.4 cm, resulting in a mesh spacing of 79.3 cm. Under normal circumstances, a mesh spacing this large should not be expected to give accurate results. However, for this HTGR benchmark, the eigenvalues for the coarse-mesh and fine-mesh methods differ by less than 0.04%. This clearly has to be a fortuitous cancellation of errors that cannot be expected in every 3-D HTGR problem.

Although the eigenvalue was well predicted in the coarse-mesh finite difference case, the power distribution predictions did not show the same cancellation of errors. Even the 6 triangles / hex finite dif-ference case with 32 axial nodes has relatively large errors (up to 5%

to 6%) in power distribution. However, the nodal option with 16 axial nodes produces a very accurate solution for a greatly reduced cost and even the nodal case with 8 axial mesh points has only 2% to 3% errors relative to the best finite difference solution.

4.3. SMALL HTGR TECT PROBLEM 4.3.1. Description of Test Problem To initiate validation of the DIF3D code for HTGR reactors, the l

DIF3D code was used to calculate a small HTGR test problem, and the results were compared with the results from other codes in use at GA.

I 4-5

909436 N/C The test problem, shown in Fig. 4-1, consists of seven fully rodded regions, each region containing seven columns. This is surrounded by one ring of reflector regions for a total of 19 regions containing 133 hexagonal columns. Each control column (regions 1 and 3.in Fig. 4-1)

~~

was loaded identically, and each standard column (regions 2 and 4 in Fig. 4-1) was loaded identically. All runs used.four neutron energy groups (three fast and one thermal). The same cross sections, for operating conditions, were used for all calculations.

Codes used in this study included GAUGE (Refs. 22 and 25), 2DB (Ref. 26), BUG 180 (Ref. 28), BUGTRI (Ref. 29), and DIF3D. .Although the small HTGR core for this study has 60-degree rotational symmetry, full core geometry was used for all codes except BUG 180. Hexagonal (triangular) geometry was used for all calculations.

~

4.3.2. Eigenvalue Results

~

Eigenvalues calculated for this rodded, seven region HTGR core are given in Table 4-3. The BUGTRI, BUG 180, and GAUGE codes solve the dif-fusion equation using mesh points at the corners of triangles. The 2DB and finite difference DIF3D codes solve the diffusion equations using mesh points at the centers of triangles. Since it was believed that a "mesh corner" code should be more accurate than a "mesh center" code, the BUG 180 code was selected to calculate the reference eigenvalue and power distribution. The LUG 180 code calculated the same eigenvalues and radial powers as the BUGTRI code for 6 and 24 triangles per hex, except that it took much less time. BUG 180 was therefore used for a calcula-tion with 96 triangles per hex. The eigenvalues calculated with 6, 24, and 96 triangles per hex were then extrapolated to obtain an estimate of the eigenvalue for an infinite number of triangles per hex.

e 4-6

909436 N/C Figure 4-1 Core Layout for HTGR Test Problem

\

> - - s'

, ,s . 4s 4 ,u . .

s

s. . . , .s s.. >...

- -(

s

,s . -

i

>- - ,/

' /

\,

s ,

• s s . . g,

,s . - , s s ,

,i s

..t 4 p.

s , 3 sp . . s,

, + . .

s , 3 .

, s

,3 . . s , -

T f

- -( y. *

, >..i s , ,

2 s

,4

, i

,y- -

, ,>- - . , , - -(

/ s ,

3

,3... s s , e

?

)

~~ ~

O

.. s..l 3 .

, s

, s s ,

-< ,N -

, s

,i . - ,-

,f y.

,i..e * ,

\ 3

- -(

4 ). . . s . . ,,

- i , 3 , *

,3.., s

• s

- 4, ,

>- , i

s. . . :,

, . . .s ,

s

s. . . g, .s

p. -

'5 - - ( -4 # 'F - core

. .(

,s . ...,

'5--'k

• l

. /

U reflector Region 1 = central region control column Region 2 = central region standard columns Region 3 = ring 1 control columns Region 4 = ring 1 standard columns Region 5 = reflector 4-7

TABLE 4-3 COMPARISON OF EIGENVALUES FOR A SMALL FULLY RLOut0 HTGR CORE Diffusion Triangles Boundary Convergence Ak -

Approximation Code Per Hex Condition (Ef) k-eff k-kref.

Mesh corner BUGTRI 6 Vacuum E-5 0.78688 -0.0069 24 Vacuum E-5 0.79176 -0.0020 Mesh corner BUG 180 6 Zero flux E-5 0.786 -0.0078 6 Vacuum E-5 0.78688 -0.0069 24 Vacuum E-5 0.79176 -0.0020 96 Vacuum E-5 0.79320 -0.0006

• -- -- 0.79379(b,c)

Mesh corner GAUGE 6 Zero flux E-5 0.78563 -0.0082 Mesh center 2DB 6 Vacuum E-5 0.80192 0.0081 7 24 Vacuum E-5 0.79616 0.0024 oo 96 Vacuum E-5 0.79464 0.0008 m -- --

0.7941(b) o,0003 Mesh center DIF3D(a) 6 Vacuum E-7 0.80188 0.0081 24 Vacuum E-7 0.79609 0.0023 54 Vacuum E-7 0.79486 0.0011 96 Vacuum E-7 0.79441 0.0006 l

0.79373(b) _o,0001 l Nodal DIF3D(a,b) 1 node Vacuum F-7 0.79468 0.0009 l per hex (a) Calculation performed on the SDSC CRAY. The other calculations were performed on the GA Technol-ogies UNIVAC.

l (b) Estimated value based on extrapolation of eigenvalue versus mesh spacing dependence.

(c Reference value. 8 w

m o

l 1

909436 N/C The extrapolated results given in Table 4-3 were determined using an assumed power law dependence of eigenvalue upon mesh spacing accord -

ing to the relation k(h) - k(0) = ch/

where k is the eigenvalue as a function of the length of one side of an elementary triangle h, and e and g are constants to be determined. k(0) is the limit of the eigenvalue as the triangle side length h approaches zero. If the definition ki = k (ht) is used and the mesh size is halved at each refinement, i.e.,

hi+1 = hi /2 then I kl .1 - kg h in (ki kl .1j in IM i 2 l

\/

and kg - k l.1 /hg 1

k(0) ~ ki+ ,

p (ij -

. 2 .

These equations were applied to the BUG 180 eigenvalues (ki=

0.78688, k2 = 0.79176, k3 = 0.79520) to obtain p = 1.76 and k(0) =

0.79379. This latter value was used as the reference eigenvalue.

Table 4-3 shows that the "mesh corner" codes approach the reference

'eigenvalue from below, i.e., with eigenvalues less than the reference value, as the number of triangles per hex is increased. The "mesh 4-9

909436 N/C center" codes approach the same eigenvalue (0.79379), except from above, i.e., with eigenvalues greater than the reference value, as e,he number of triangles per hex is increased. This gives strong evidence that the.

BUG 180 extrapolated eigenvalue (0.79379) is very close to the "true" eigenvalue for this seven region HTGR core.

Once this reference eigenvalue has been determined, then the eigen-value from the nodal DIF3D can be compared to it. The very small dif-ference between the nodal DIF3D eigenvalue and the reference value (Ak =

0.0009) indicates that the nodal DIF3D code does a very good calculation of the eigenvalue for this test case. The difference is so small, in fact, that to obtain a similar Ak from a finite difference calculation (BUG 180, 2DB, or DIF3D) would require either 54 or 96 triangles per hex.

Table 4-3 also gives the results of a GAUGE calculation of the HTGR test problem. The GAUGE results (Ak = -0.0082) are very close to the results from the BUG 180 calculation (Ak = -0.0078) with six triangles per hex and a zero flux boundary condition, as would be expected. How-ever, the GAUGE Ak = 0.0082 is much larger than the nodal DIF3D Ak =

0.0009. Since the three-dimensional GATT code uses the same six trian-gles per hex and the same solution technique as the GAUGE code, it is reasonable to expect a three-dimensional nodal DIF3D calculation of k-eff to be as good, if not better than, a three-dimensional GATT calcu-lation of i-eff.

4.3.3. Radial Power Distribution Resul,ts Table 4-4 gives the average power densities and radial peaking fac-tors for the four core regions shown in Fig. 4-1 obtained by eight of the calculations listed in Table 4-3. A vacuum boundary condition was used for all calculations in Table 4-4, except the GAUGE calculation which used a zero flux boundary condition. This GAUGE calculation used a central point weighting factor of 0.5. The radial power density was normalized to 1.0 over the core in all calculations.

4-10

909436 N/C TABLE 4-4 RADIAL POWERS FOR A SMALL FULLY RODDED HTGR CORE

., Triangles Average  % Difference Peak to  % Difference Code Per Hex Region Power Density From Reference Average. Power From Reference BUG 180 6 1 0.4267 1.9 1.1070 -9.0 2 1.0750 -6.5 1.0975 2.3-3 0.3899 8.3 1.1427 -12.7 4 1.1051 0.7 1.5660 2.0 BUG 180 24 1 0.4207 0.5 1.1901 -2.2 2 1.1335 -1.4 1.0743 0.2 3 0.3664 1.8 1.2695 -3.0.

4 1.0995 0.1 1.5404 0.3 i

BUG 180 96 1 0.4186 1.2153 2 1.1496; Reference 1.0726L Reference 3 0.36001 Values 1.30891 Values 4 1.0979 1.5354

., GAUGE 6 1 0.4085 -2.4 1.1696 -3.8 2 1.0985 -4.4 1.0851 1.2

, 3 0.3697 2.7 1.2155 -7.1 4 1.1950 0.6 -1.5663 2.0 DIF3D 6 1 0.4012 -4.2 1.2107 -0.5 2 1.2021 4.6 1.0562 -1.5 3 0.3347 -7.0 1.3127 0.3 4 1.0938 -0.4 1.4230 -7.3 DIF3D 24 1 0.4133 -3.3 1.1772 -3.2 2 1.1684 1.6 1.0669 -0.5 3 0.3514 -2.4 1.2693 -3.0 4 1.0963 -0.1 1.4681 -4.4 DIF3D 96 1 0.4165 -0.5 1.1888 -2.3 2 1.1584 0.8 1.0700 -0.2 3 0.3562 -1.1 1.2809 -2.1 4 1.0971 0.0 1.4972 -2.5 Nodal 1 node 1 0.4186 0.0 1.1762 -3.3 DIF3D per hex 2 1.1865 3.2 1.0629 -0.9 3 0.3473 -3.5 1.2851 -1.8 l* 4 1.0938 -0.4 1.4428 -6.0 l

l 4-11

1-909436 N/C 1

The BUG 180 with 96 triangles per hex was assumed to be the refer-ence power distribution. The finite difference DIF3D with 96 triangles per hex gave a very similar power distribution to the reference values.

The "mesh corner" BUG 180 code produced powers which approached the ref-erence values, as the number of triangles increased, with the powers tipped up toward the core edge. The "mesh center" finite difference DIF3D powers approached the reference values in the opposite manner, with the povars tipped down near the core edge, as the number of trian-gles was increased. This gives strong evidence that the reference power values are very close to the "true" values for this seven region HTGR Core.

The nodal DIF3D produced region powers and peaking factors which are in reasonable agreement with the reference values. The nodal DIF3D values fall between the finite difference DIF3D values produced with 6 and 24 triangles per hex. The nodal DIF3D powers tip down near the core edge, and out of the control columns toward the standard columns, rela-tive to the reference values.

The powers calculated with the GAUGE code are more similar to the BUG 180 code. This is reasonable since both codes use a "mesh corner" colation technique. The GAUGE powers tip up toward the core edge as do the BUG 180 powers.

The ratio between the average ring 1 powers for the nodal DIF3D and the GAUGE is (0.3473 + 6 x 1.0938)/(0.3697 + 6 x 1.1050) = 0.987; i.e.,

the nodal DIF3D power for ring 1 is 1.3% less than the GAUGE ring 1 power. For large cores, this difference between the nodal DIF3D and GAUGE outer ring powers might be larger, because the outer ring would be

,' a smaller fraction of the core.

What has been said above for the nodal DIF3D versus GAUGE compard-son of two-dimensional calculation results should also apply, in a gen-eral sense, to three-dimensional calculations using the nodal DIF3D and 4-12

909436 N/C GATT codes. This is because the GATT code uses the same solution tech-nique to calculate the radial power distribution as the GAUGE code, except that the GATT code also includes the axial dimension.

4.4. VALIDATION OF CRAY VERSION OF DIF3D 4.4.1.' DIF3D Conversion to CRAY Version 4.0 of the DIF3D code was obtained from the National Energy Software Center (NESC) at Argonne National Laboratory (ANL) early in 1986. It was put on the San Diego Supercomputer Center (SDSC) CRAY X-MP/48 computer using Version 113 of the CFT FORTRAN compiler. In August 1986, Version 5.3 of the DIF3D code was obtained directly from ANL, and prepared for the CRAY using Version 114f (dated July 31, 1986) of the CFT FORTRAN compiler. The additional capabilities in Version 5.3 of the DIF3D code includes

1. Upscatter in the two- and three-dimensional hexagonal geometry nodal options.

2. Diffusion theory and transport theory Cartesian geometry nodal options.

3. Updated versions of the FORTRAN 77 I/O subroutines that were found necessary in Version 4.0 of DIF3D.

Version 5.3 of the DIF3D code on the CRAY passed through six edi-tions between August and November 1986 as relatively minor changes were found to be necessary. At various points in this process, test calcula-

,' tions were done in order to find and fix prob 12ms in the edition current at that time. These test calcalations are also useful to help validate

~

use of the DIF3D code on the SDSC CRAY computer.

4-13

909436 N/C 4.4.2. Validation Results A preliminary three-dimensional (3-D) model at the beginning of Cycle 4 of~the FSV HTGR was set up and run with Version 4.0 of the DIF3D code on the SDSC CRAY X-MP/48 and on an IBM-3090 Model 200 at Public Service Company of Colorado (PSC), and with Version 5.3 on the CRAY.

Eigenvalue results for this preliminary problem are given in Table 4-5.

These eigenvalues show that a reasonable DIF3D model was set up that gives the same results on two very different computer systems, and that Versions 4.0 and 5.3 give the same results. These particular calcula-tions do not have the correct fission spectrum and control rod posi-tions, so that the eigenvalues in Table 4-5 are not correct for any par-ticular time point. Both the IBM and CRAY results for Version 4 given in Table 4-5 are for one-group of neutron fluxes at-a-time in core. The calculation for Version 5.3 was entirely core contained.

Other 2-D and 3-D results of DIF3D calculations for Cycle 4 of FSV are given in Ref. 30. This reference makes comparisons between DIF3D and other codes, which is also done in Sections 4.2 and 5 of this report.

Ten test problems supplied by ANL were t us with editions 1 and 4 of Version 5.3 of DIF3D on the SDSC CRAY X-MP/'+8 computer. Each edition was used to calculate all ten test problems. Within the requested con-vergence, editions 1 and 4 calculated identicaA results. The CRAY results were also in very good agreement with the ANL DIF3D-5.2 results (Table 4-6). This indicates that edition 4 of Version 5.3 was correctly converted to the CRAY.

," Edition 5 replaced edition 4 of Version 5.3 of tne DIF3D code on October 30, 1986. The only change was the repair of an omission in edit subroutine BALINT so that the first part of the new normalized NEUTRON balance edit would be done even when the "region balance edit by group" l option is turned off. The region balance edit by group is volumfr.ous and not very informative in large 3-D problems.

4-14 h

09436 N/C TABLE 4-5 EIGENVALUES CALCULATED BY A NODAL DIF3D USING A PRELIMINARY 3-D MODEL OF FSV Organization Computer Code Eigenvalue PSC IBM-3090, Model 200 DIF3D-4 1.0075003 GA SDSC CRAY X-MP/48 DIF3D-4 1.0075004 GA SDSC CRAY X-MP/48 DIF3D-5.3/Ed2 1.0075004 e

• i i

l 0

4-15 l

l

TABLE 4-6 EIGENVALUES CALCULATED FOR ANL TEST PROBLEMS Problem genva ues No. Geometry Method ANL GA PSC 1 2-D triangular SNR FD06 1.1272804 1.1272802 1.1272804 2 2-D hexagonal SNR nodal 1.1252866 1.1252893 1.1252866 3 3-D her-Z SNR nodal 1.0115059 1.0115057 1.0115059 4 3-D tri-Z SNR FD0636 1.0128036 1.0128034 1.0128036 5 2-D X-Y IAEA FD 1.0294798 1.0294795 1.0294798

, 6 3-D X-Y-Z IAEA FD 1.0290562 1.0290562 1.0290562 h 7 2-D X-Y Nodal diffusion 1.1107247 1.1107245 1.1107247 8 2-D X-Y Nodal transport 1.1154839 1.1154836 1.1154839 9 3-D X-Y-Z SNR nodal diffusion 1.0168369 1.0168367 1.0168369 10 3-D X-Y-Z SNR nodal transport 1.020573(a) 1.0205467 1.0205468 Computer: IBM-3090 CRAY IBM-3090 Model 200 X-MP/48 Code: DIF3D-5.2 DIF3D-5.3/ DIF3D-5.3 ed 1 and 4 Date: 9-14-85 9-19-86 and 10-13-86 (a)ANL results for test problem 10 are not fully converged, because the calculation exceeded e the maximum time limit. 8 0

m

, o I

909436 N/C

' Edition 6 replaced edition 5 of Version 5.3 of the DIF3D code.

Edition 6 uses a new FORTRAN library (NFORTLIB) in which the previous limit of about 262E+03 (decimal) words per logical record has been increased to about 268E+06 (decimal) words. The additional coding to handle atom density files (ZNATDN) exceeding 1.06E+06 (decimal) words in one logical record was removed from the REED / RITE subroutines in edi-tion 6. Subroutines RREAD/RWRITE were then modified to use the more efficient RDBIN/WRBIN FORTLIB I/O subroutines.

After each change a full-sized 3-D nodal problem was restarted to confirm that the change was correct.

4.5. VALIDATION OF IBM VERSION OF DIF3D The first version obtained by PSC from NESC (National Energy Soft-ware Center) was Version 4. This version was installed and yielded the results shown in Table 4-5. This version, however, ultimately produced problems for FSV 3-D problems only with respect to the PSC IBM operating system. It is thought that these problems were the result of some of the assembler routines running under the PSC operating system. After discussing these problems with NESC, it was concluded that Version 5.3 of the ccde, with its decreased reliance on ASSEMBLER, would correct the problem.

Version 5.3 was obtained from Argonne and compiled in December 1986. As was expected, this version eliminated the previous problem concerning the 3-D FSV problem. The ten sample problems were success-fully run. The eigenvalue results are listed in Table 4-6.

The PSC eigenvalues compare exactly with the ANL results for sample problems 1 to 9. For sacple problem 10, the PSC eigenvalue (fully con-verged) is almost identical to the GA value in sample problem 10.

4-17

909436 N/C

5. VALIDATION OF FSV MODEL 5.1. FSV CYCLE 3 BURNUP The primary method of validating the ncdal DIF3D code for HTGR calculations is through 3-D burnup calculations of the Fort St. Vrain (FSV) core. These calculations were done for Cycle 3 from 170.4 effec-tive full power days (EFPD) to 294.5 EFPD. This time interval was selected because of the long period of stable power production at about 589 MW from 221.0 to 282.7 EFPD. The end of this stable power period was expected to have some of the best measurtments of core outlet tem-perature for comparison to the DIF3D calculsted radial powers. The nodal DIF3D results were compared to finite uifference GAUGE and SUGTRI code results in two dimensions, and to the finite difference GATT code results in three dimensions.

The designed full power rating of the FSV reactor is 842 MW thermal and 330 MW electrical. The third cycle of operation took place between July 15, 1981, and January 20, 1984.

At the end of each month, the operating power history of the FSV core is complied by Public Service Company of Colorado's Technical Serv-ices organization at the reactor site. This history provides the aver-age hourly thermal power generation for each day of the month. Except during power transients, the important core parameters (heavy metal inventory, region peaking factors, excess reactivity, control rod con-

. figuration, etc.) do not change appreciably during burnup intervals of a few days. Consequently, it is not necessary to model the "official" power history by each hour, or even each day. The power history is reduced to a manageable number of time intervals suitable for burnup calculations with the Fuel Accountability (FA) GAUGE model. The model 5-1

.t" 909436 N/C used for the FA calculations in the finite difference GAUGE (Ref. 22)

, code has been used extensively since the beginning of the initial cycle to monitor fuel and core performance, as well as producing a technical data base for reload segment SARs.

The simplified power history used ir. the FA GAUGE calculations, as well as the cumulative energy production in Cycle 3, 1s given in Table 5-1. The column heading "RR" stands for the regulating rod in region 1, and "Shim" is the partially inserted control rod shim bank in the Cycle 3 withdrawal sequence. The control rod withdrawal sequence in Cycle 3 is given in Table 5-2. The "Time Point" in Table 5-1 is the

-number of the FA GAUGE calculation at the end of the time interval which is written to a magnetic tape. Time points 640 and 650, for which k-eff values are given, will be discussed further in Section 5.2. The GAUGE

. calculations were done eith three fast and four thermal energy groups.

For three-dimensicaal calculations, the 22 burnup intervals in Table 5-1, that were used in the GAUGE code, were reduced to the seven burnup intervals in Table 5 3. Using these seven intervals, the 3-D GATT code was used to calculate the fuel burnup for each fuel element.

For this current study, the calculations using the seven time intervals of Table 5-3 were repeated, except using 3-D nodal DIF3D calculations instead of the GATT calculations.

5.2. CALCULATIONAL SEQUEFCE 5.2.1. 2-D Calculations The GAUGE code (Refs. 22 and 25) is a two-dimensional hexagonal

. geometry code based on the finite difference approximation to diffusion theory. GAUGE uses six triangles per hex with the mesh points at the corners of the triangles. Each hex represents one column of fuel ele-ments in the FSV reactor. To perform fuel accountability (FA) calcula-tions for FSV using GAUGE, seven-group microscopic cross sections are 5-2

-9 - - - e -- - -- ,-w -

.1 TABLE 5-1 FSV POWER HIbTORY USED IN CYCLE 3 FUEL ACCOUNTABILITY GAUGE CALCULATIONS FSV Cycle 3 Power History FA GAUGE Burnup Interval End of Interval Date MW-HR EFPD Days Power, MW RR(a) Shim (a) Time Point k-eff 05/24/83 at 2100 3,442,878 170.4 06/07/83 at 2400 3,457,628 14.1 43.5 115 2A at 114 612 06/13/83 at 1800 3,472,808 5.8 110.0 115 4D at 113 614 06/23/83 at 2400 3,472,808 10.3 0.0 115 4F at 65' 616 07/07/83 at 1200 3,510,500 13.5 116.3 115 4D at 134 618 07/11/83 at 2400 3,510,500 4.5 0.0 115 4F at 112 620 07/15/83 at 2400 3,517,654 4.0 74.5 117 3C at 102 622 07/31/83 at 2400 3,786,790 31.4 357.2 117 3C at 102 624 08/18/83 at 1800 4,029,610 17.8 570.0 118 4B at 134 626 08/31/83 at 2400 4,194,948 13.3 519.9 118 4B at 190 628 09/06/83 at 2400 4.283,998 6.0 618.4 118 3D at 49 630 09/08/83 at 2400 4,318,270 2.0 714.0 118 3D at 76 632 I"

09/30/83 at 2400 4.611,310 22.0 555.0 117 3D at 72 634 10/12/83 at 2400 4,769,710 12.0 550.0 113 3D at 75 636 10/29/83 at 0900 4,999,221 247.4 16.4 584.0 116 3D at 96 638 11/03/83 at 0600 4,999,221 4.9 0.0 116 2A at 123 640 1.0071 11/13/83 at 2400 5,070,519 10.8 276.4 116 4B at 87 642 11/30/83 at 2400 5,313,687 17.0 596.0 116 3D at 95- 644 12/08/83 at 0600 5,417,232 268.1 7.3- 595.1 116 3D at 101 646 12/11/83 at 0600 5,417,232 3.0 0.0 118 3D at 110 648 12/31/83 at 2400 5,710,638 282.6 20.8 589.2 118 3D at 110 650 1.0094 01/17/84 at 0900 5,933,862 16.4 568.0 116 3D at 126 652 01/20/84 at 1200 5,951,457 294.5 2.9 255.0 108 3D at 56 654 (a) Inches withdrawn.

it

?

E a

909436 N/C

• . TABLE 5-2' FSV CONTROL ROD WITHDRAWAL SEQUENCE FOR CYCLE 3 Withdrawal Sequence Group Regions 1 23 3,5,7 2 4A 20, 26, 32 3 4C 22, 28, 34 3A 1 (half out) 1 4 4E 24, 30, 36 5 4F 25, 31, 37 6 2A 2,4,6 7 4D 23, 29, 35

, , 8 3A 8, 12, 16 9 3C 10, 14, 18 10 4B 21, 27, 33

_ 11 3D 11, 15, 19 12 3B 9, 13, 17 13 1 (last half) 1

. Number of Rodded Regions Tim SW Point Position Fully Inserted Partially Inserted 640 2A at 123 18 4 650 3D at 110 3 4 O

e 5-4

909436 N/C

. . TABLE 5-3 POWER HISTORY USED FOR 3-D CALCULATIONS IN CYCLE 3 WITH GATT AND DIF3D Time Point for 3-D Calculacions Core Burnup Calendar Core Shim Bank Interval (EFPD) Days Power, MW Position (a) Beginnir.g End 170.4 to 180.0 22.4 357.2 3C at 2/6 20 21 180.0 to 200.0 29.8 570.0 4B at 1/6 22 23 200.0 to 221.0 -31.3 555.0 3D at 3/6 24 25 221.0 to 247.5 38.16 589.0 3D at 3/6 26 27 247,5 to 268.2 29.57 589.0 3D at 2/6 28 29 4 . 268.2 to 282.7 20.75 589.0 3D at 2/6 30 282 7 to 294.5 17.67 568.0 3D at 2/6 31 32 (a) Fraction Inserted. Regulating rod position in region 1 was kept at a constant insertion position of two out of six fuel layers, i.e.,

2 x 31.22 in. = 62.44 in. inserted or 4 x 21.22 in. = 124.88 in.

withdrawn.

5-5

909436 N/C devel> ped with INTERP at four temperatures (300, 600, 900, and 1200 K)

, for the C/Th and C/U ratios at the beginning of a cycle. Atom densities are obtained from the FA GAUGE calculations from the previous time interval. FSV reactor data, recorded by the data logger, is analyzed by the FSVCOR code to give control rod positions and region temperatures for each time point. Then the MUGE code, using the input atom densi-heies and input fuel and moderu;or temperatures for each region, inter-polates between the four temperature microscopic cross sections to cal-culate the macroscopic cross sections for each region for the correct temperatures at that time point. The GAUGE code, using the newly gener-ated macroscopic cross sections, then calculates the k-eff and radial power distrivation for that time point. It can also be continued with a burnup and a diffusion calculation at the next time point with new con-trol rod positions and new temperatures. This is the procedure that was used for the calculatior.a that are listed in Table 5-1.

For this DIF1D validation effort, the GAUGE calculations at time points 640 and 650 were reran to obtain the region macroscopic cross sections for later use in 2-D DIF3D and BUGTRI calculctions. Time points 640 and 650 wera chosen because they represent cold critical and hot operating conditions, respectively. It was also thought that the FSV regi.n gas outlet teuperature measurements should be reasonab1v accurate at time point 650 due to the previous 61.7 EFPD of high. power operation. The fuel accountability GAUGE calculations (Table 5-1) were done with doubled reflettor impurity ator 'ensities to correct for known discrepancies in the GAUGE calculated re. power distriLution. But to permit direc; compacison between reactor measurements and "uncccrected" calculations for 'e as-built design, the macroscopic cross sections tenerated for timu points 640 and 650 used the as-built reflector impur-ity .ta density. These macrorcopic cross sections generated by GAUGE ver -

sed in BUGTRI and DIF3D cs.lculationa for time points 640 and old critical and hot operating conditions. The k-eff results

.. in Table 5-4.

l 5-6

TABLE 5-4 COLD / HOT 2-D CALCULATIONS IN SEVEN GROUPS Atom 'ensities k-eff for k-eff for Diffusion Triangles for Reflector Cold Critical Hot Operating Cold-to-Hot Code Apprcximation Per Hex Impurities (TP 640) (fP 550) Ak GAUGE Mesh corner 6 Doubled 1.0071 1.0093 0.0022 GAUGE Hesh corner 6 As-built 1.0102 1.0123 0.0021 BUCTRI Mesh corner 24 As-built 1.0096 1.0103 -

0.0007 DIF3D Mesh center 6 As-built 1.0113 1.0094 -0.0019 DIF3D Mesh center 24 As-built 1.0100 1.0097 -0.0003 DIF3D Nodal 1 As-built 1.0090 1.0088 -0.0002 Linearly extrapolated values:

Mesh corner Infinite As-built 1.0090 1.0083 Hesh center Infinite As-built 1.0087 1.C100 Average of extrapolated values: 1.0089 1.0092 0.0003 Nodal DIF3D - Average extrapolated value:

• 0.0001 -0.uu04 o

.g

?

21:

o i

i

.. . - ~ . . m . - _

it.,

& ~

e 909436 N/C I

5. 2. 2. D Calculations.

Three-dimensional'burnup calculations were done for Cycle 3 of the H FSV reactor'between 170.4 EFPD and 294.5 EFPD using the calculational s.

' sequence lLn Fig. 5-1. This is basically the same calculational sequence as used for previous 3-D fuel accountability calculations, except that the DIF3D code was used to calculate the 3-D fluxes rather than the GATT code. This allows the direct comparison of results between the current DIF3D validation calculations and the previous GATT fuel accountability calculations.

The calculational sequence in Fig. 5-1 begins with the FSVCOR code,-

which reads the data tape prepared by the FSV-data logger. This tape contains the:FSV cassurement data.ct each measurement time point. From the measured values of the coolant flow rate, the region orifice set-tings,'and the region gas outlet temperatures, the radial peaking fac- .i tors (RPFs) can be calculated for most regions. For regions 20, and 32 through 37, the gas outlet temperatures are believed to be very inaccu-rate due to cold gas streaming along 'he~ thermocouple string. There-fore, GAUGE calculated RPFs are read into FSVCOR for these regions and used for the core power normalization. Consequently, a comparison of measured and calculated RPFs for these regions is not meaningful.

t POKEGT reads in the core coolant flow rate and inlet temperature, and the region orffice setting and gas outlet temparature. The control rod positions are also read in for each region. Precomputed axial power distributions for each region then permit POKEGT to perform an axial thermo-hydraulic calculation for an average channel in each core region.

The calculated results are the average fuel and moderator temperatures

.; for each fuel element.

i l

The GATMAC code reads in the average temperatures for the top, side, and bottom reflectors. Using precomputed graphite cross sections at 300, 600, 900, and 1200 K, the code interpolates between the fixed 5-8

, . . , f 1 c

l l

909436 N/C l

- ; Fig. 5-1.. -.GA, coquence for ~3-D calculations with DIF3D Data from Data Logger

( FSVCOR ) '

Inlet, Outlet &

Power, Mass Flow, Side. Reflector RPFs, Control Rods Temperature Temperature Dependent

( POKEGT

) ( GATMAC _)

4 Group , ,

Microscopic Region Fuel and- Reflector Cross Sections Moderator Temps. Macros Nuclide Densities j Jor Each Burnup 3, GZINT f Region at BOI 3 Microscopic Cross Sections for Each Nuclide for Each Burnup Region

(Static BUGATT): (GEOMETRY )

Macroscopic Cross Section7 for Each Region

] (Nodal DIY3D at BOI'r 4 Group Fluxes Power at Each Node Each Node BurnupBUGATT) ( .DIFPOW

- _.L.

Densities Macros Radial and Axial

-_a_t EOI et EOI F ser Distribution I 1 1

( 2Vi.f.,ED } Nodal F3D

( RPT

)

' Fuel Accr.untability P3 dial Peaking by Block

,Fo:ctor Comparisons

( FIMA ) BOI = Beginning of Intervsl EOI = End of Interval .

Maximum Block Burnup 5-9  ;

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

909436'N/C temperature cross sections to obtain the reflector cross sections at the correct temperatures.

The GZINT code reads in precomputed four group microscopic cross sections for five fuel temperatures (300, 600, 900, 1100, and 1300 K) and five moderator temperatures (300, 600, 900, 1050, and 1200 K). 'The average fuel and moderator temperatures for_each element calculated by POKEGT are then used to calculate the microscopic cross sections for each nuclide for each fuel element at the correr- fuel and moderator temperatures. These microscopic core cross sections, together with the macroscopic reflector cross sections from GATMAC, are then transferred to the BUGATT code.

A static BUGAT*i calculation is done at the beginning of the burnup

, interval to calculate the macroscopic cross sections for each fuel element. To do this, nuclice densities for each fuel element are read in from the end of the previous 3-D burnup interval. The GEOMETRY code is used to prepare the input data to define the burnup region number for each fuel ele 2ent. This is used by the BUG /.TT and DIF3D codes.

The macroscopic cross sections for the fuel elements and fcr the reflectors are read into the DIF3D code. The DIF3D code is used to cal-culate the four-group fluxes for the 3-D model of the FSV reactor. This is a static calculation, i.e., at only one time point. There is cur-rently no option to do burnup calculations within DIF3D. All 3-D DIF3D calculations used the nodal option with one radial node per hex and two axial nodes per fuel element. For comparison, the 3-D GATT code used for the previous fuel accountability calculations used six triangles per hex and eight axial points per fuel element.

The four-group fluxes for each node calculated by DIF3D are read 4 into the BUGATT* code, and a burnup calculacion is done. Each burnup region (consisting of one or more FSV fuel elements) uses the group

- fluxes averaged over all nodes in the burnup region to deplete the atom 1

7 5-10 L -.

. 909436 N/C densities over the burnup interval. Atom densities and macroscopic cross sections are then calculated for each burnup region at the end cf the burnup interval. These macroscopic cross sections are input directly into another nodal DIF3D to calculate the k-eff and node powers et the and of the burnup interval. The node powers calculated by DIF3D are analyzed by DIFPOW to produce the axial peaking factors for each region, and the radial peaking factors (RPFs) for each column. The RPFs are input to the RPF code which produces figures (Appendices A, B, and C), comparing RPFs from DIF3D, GATT, FSVCOR, etc.

If the temperatures and control rod positions do not change, e.g.,-at 268.2 EFPD in Table 5-3, the enc of interval DIF3D fluxes are inserted into a BUGATT for the next burnup interval. If temperatures or control rod positions do change, which is usually the case, GZINT and a

, static BUGATT must be run using the end of interval atom densities from the last burnup BUGATT in order to calculate new macroscopic cross sec-

,, tdons for the next burnup interval. When all burnup intervals are com-pleted, the atom densities at the end of the last burnup interval are read into the FUELED code. This code calculates the burnup and nuclide weights for each element in the FSV core. The FIMA code analyzes the FUELED results to determine the fuel elements with the maximum burnups for each segment and each layer.

Figure 5-1 shows the calculational sequence performed by GA Tech-nologies on the CRAY X-MP/48 at the San Diego Supercomputer Center (SDSC). The calculationsl sequence that would be performed by Public Service Company of Colorado (PSC) on their IBM for 3-D fuel accountabil-ity is shown in Fig. 5-2.

.' The FSVCOR code in Fig. 5-1 is replaced by a POKE (Ref. 31) calcu-lation in Fig. 5-2. The FSVCOR code i data reduction code which was derived from the POKE model. FSVCOR .. apecific to the FSV reactor, while POKE is a more general code. The two codes give nearly identical output (differences ( 0.5%) for the same probicm. These differencas 5-11

909436 N/C Fig. 5-2. PSC sequence for 3-D_ calculations with DIF3D Data from Data Logger

( POKE )

• Inlet, outlet &

. Power, Mass Flow, Side Reflector RPFs, Control Rods , Temperature Temperature Dependent

( POW ) ,

4 Group Microscopic Region Fuel and Cross Sections, Moderator Temps.

Nuclide Densities for Each Burnup ( GATZINT }

Region at BOI .

Microscopic cross Secticas for Each Nuclide for Each Burnup Region

(Static BUGATT) (GEOMETRY )

Macroscopic Cross Sections for Each Region (Nodal DI 3D at BOI'E .

4 Grou Fluxes Power at Each N de Each Node

~

' Burnup BUGAT*

( DIFPOW )

Densities Macros Radial and Axial at EOI at E0I Power Distribution f } l

( FUELED } Nodal F3D

( RPF

]

Fuel Accountability RadLal Peaking by Block Factor Comparisons BCI = Beginning of Interval E0I = End of Interval P

5-12

909436 N/C 183 101 IE5 164 IC8 20 154 152 27 100 38 158 38

1. 99 35 ts7 105 181 159 183 21 ISO 64 8 103 102 154 $7 IS tot 157 la 93 109 tt G1 158 155 M- 9 65 107 108 48 2 113 153 7 60 112 153 17 to 23 33 #- 43 10 63 III 152 151 g7 42 33 3 47 g fl0 14 6 SE 8 41 33 115 116 147 86 43

.. 16 24 22 72 11 117 gg g 148 51 4 194 145 g4 7 g 7 5 55 142 143 83 15 IIS 120 g

' I 145 15 12 121 144 13 73 118 7, 7 133 1:3 14 82 124 77 j 30 gg 127 123 , 125 141 131 26 l'1 135 27 122 134 135 23 128 123 29 130 !32 123 137 133

• - Columns used in Table 5-21.

Fig. 5-3. Fort St. Vrain core layout - numbers represent burn'ep regions for 2-D caleclations, and for the bottom core layer of 3-D calculations 5-14

t

e -

909436 N/C arise principally due to the slight differences in modeling the axial '

power profile. The FSVCOR code performs a more complete primary side heat-balance than POKE. FSVCOR also calculates core inlet temperature and flew. POKE requires these as input. On the other hand, POKE can be used as a design code, whereas FSVCOR is strictly a data reduction code.

The GATMAC and GZINT codes used at GA are combined into one code, GATZINT, at PSC. PSC does not hsve the GA RPF code, but has a similar type of code for producing RPF comparisons. PSC also does not have the FIMA code.

5.2.3.. DIF3D Model The active core of the FSV reactor consists of 37 fueled regions.

. Thirty-one regions have seven :olumns and six regions have five columns.

Each column is a stack of six fuel elements. Figure 5-3 shows the 2-D model of the FSV core in hexagonal geometry. This is the model used in the GAUGE, BUGTRI, and 2-D DIF3D calculations summarized in Table 5-4.

The numbers in F.! 4 5-3 are the burnup region numbers. Hexes with the same burnup region number are depleted with fluxes averaged over all hexes with that number. Combining several elements into the same burnup region was to reduce the computer memory storage. On the modern machines this requirement is not necessary. In the future the FSV model will be updated, such that each element is represented by its own burnup region. The radial reflectors outside the active core that are used in the code models are not shown in Fig. 5-3.

The model used in the 3-D DIF3D calculations is shown in Fig. 5-4.

Each core element is divided into two axial slices, with each axial

.' slice containing or.e axial node in the nodal option. This arrangement is necessary, because the bottom control element in each control column is only three-fourths cs long as the standard element or the other con-tro'. elements. The 37 core regions in the bottom core layer (slice 3) are numbered 1 through 169, in the same pattern as Fig. 5-3. The burnup 5-13

ll$.

909436 M/C Figure 5-4 Axial 3D Geometry in Nodal DIF3D for Fort St. Vrain

. Slice' cm 635.8 30 Wt% Rodded 40 Wt% Rodded l- Reflector Reflector-(Unrodded Reg. #1018) (Unrodded Reg. I1010) 54 .8 urvnaaaa mnn r' a r l a ,, e n e in17 8

516.0 t i

13 Regions l Regions 883-1014 I846-882 12 456.5  % l 8 436.7 p $

I y' y Regions l Regions $ o 1 -845 1677-713 ^ y 377.2 "

0 357.4 ,, o O a v g o o g

Regions g Regions o  %

297.9 ,

545-676 ,508-544 w e u .

_ o a 8 278.1 l,

5 y

.. o Regicns l Regions 3 3 7 376-507 1 339-375 0 y 218.6  : o A

6 198.8 ,,

a 5 Regions I Regions 207-338 1 <

139.3 E l170-206 4 119.5 3 3 Regions Regions l

38-169 1-37 l 2 60.0 Buccum Refleu$vt A016 50.0 1 Bottom Reflector 1015 0.0 _

Region Number t

(.

• Axial Slice Unrodded 30 Wt%

Rods 40 Wt%

Rods A t l

I I

16 1018 1021 1023 15 1017 1022 1024 v h

'4 1017 1022 1024 Uncontrolled Control l Regions Regions 5-15 ,

I

909436 N/C region number for each element in slice 5 is 169 higher than the element

,. below it. The burnup region numbers progress similarly until, at the top (sixth) layer of the core, the largest burnup region number in the core is 6 x 169 = 1014. The 3-D DIF3D calculations used vacuum boundary conditions at the outer radial boundary and at the lower and upper axial boundaries.

5.2.4. Differences Between DIF3D and GATT Calculations The GAUGE and GATT codes require complete rings of seven-column regions, and zero flux boundary conditions. The requirement of having complete rings means that a low-density graphite region had to be used radially outside the borated side reflector (Fig. 5-4) in the GATT cal-culations for FSV. The DIF3D code geometry is specified using rings of

, a single hexagons; however, these rings do not need to be complete.

This allows the omission of the low-density region radially outside of the borated side reflector that is used in the GATT calcu'.ations. The DIF3D code is also not restricted to zero flux boundary conditions.

Therefore, to increase the speed and accuracy of the 3-D DIF3D model used in the DIF3D validation calculatiens, the low density graphite region was removed and a vacuum boundary condition was used.

The effect of these model changes is shown in Table 5-5 for calcu-lations at 4.9 EFPD into Cycle 4 of FSV. Table 5-5 indicates that the difference in the calculated eigenvalue due to the model changes is less than 0.0001. Figure 5-5 shows that the change in the radial power dis-tribution is less than 1%. Figure 5-6 shows that the change in the axial power distribution in the core is at most only 1%. Since the vacuum boundary condition should simulate reality better than the zero

, flux boundary condition, the 1% higher power density in the top core

. layer should also be closer to reality. Measurements of axial power or burnup, however, are not within 1% uncertainty.

5-16

909436 N/C TABLE 5-5 3-D MODEL COMPARISON USING NODAL DIF3D AT 4.9 EFPD, CYCLE 4 0F FSV DIF3D No. 1 DIF3D No. 2 3-D model Same as GATT Same as Fig. 5-4 Number of regions 1025 1024 With low density. graphite region Yes No outside borated side reflector Boundary conditions Zero flux Vacuum k-eff 1.019845 1.019928

.. Ak - 0.000083 ,

e s

6 9

5-17 i

Figure S-5. 3D Nodal DIF3D flodels to Determine Effect of Exterior Low Density Region i

Exterior Region Vacuum Boundary f=0 B.C.

Condition j Borated Reflcctor

,s 1 l .,..

'p*w* r l y.:

(ew < -

- y ~ ' a. ..'S h a. ' } :.',

p y- v '  %. g i

a

...t , %.6 }> 5 r. . $- ,96

• 4

\ <- . ,, s "p V + ,.

~

y_ l ' ,5 'y' gyb 5 'g 'Y

. ti , . '5

- '. 41, b -

.. ... ..4, u, .

,r. . .n.

7-p. ,+  ; * . ,

[i. -

, .2 '.,

' ' , M . -

, . .e Reflector

- f [. . /. .

,. ,.(* .

t

',',.. ' . . t'*

,51 ' .'

,'. '6 - l

,..a ,

',< - i.

?g!,Q ',.

. e

~'

a 5 ~ ,

, .2 .2 '

l~d '.' . ,

,' ~ .~ N

(

,.. ',' . .t' ,5E;

• ' .,..t,' "

l ,--(,

• M '

1 .77 's . .

'/. . . .1' ty '.

.77 , ~'s, . ~~Y ,

, . . t'

. - -C.

i .I.00 ~.~Y.

• V7 -: tr'.. C

. : ,, ,', . ." ~-8

.w. -

l Power Density (w/cc) at Core Midplane L . . r, ,

(n

, 1 Difference in

{ Pouer Density Due i to Removal of Exterior Low Density Region 4

d

909436 N/C Fig. 5-6. Effect of Exterior Region Removal ,

Absorption Rate with Exterior Region 3

(% Difference Without Exterior Region) a Power Density (w/cc) Rodded: Rodded:

at Core Centerline 1.52+16 (+1.5%) 1.37+16 (+1.7%)  !

With No Unrodded; 1.87+16 (+1.5%) l Exterior Exterior Region Region,A Unrodded: 4.28+15 (+0.004%) l I

0.54 1.01%

l I

l

, 0.84 0.25%

l l

l 1.08 -0.05%- 1.06+1 7- l

(+0.09 %)$ 7i 1

5l 1.24 -0.18% e, Ol 7 $!

5 .

1l

~

0.99 -0.22% l 8

ac4 m

0.69 -0.17% g 4

L 2.65+15 (+2.6%) fo u=l

~

7.89+15 (+6.8%)

5 5-19

l 909436 N/C 5.3. REACTIVITY COMPARISON 5.3.1. 2-D Raactivity Comparison The two-dimensional calculations summarized in Table 5-4 were made to investigate the e.alculated-to-measured k-eff discrepancy at cold critical and hot oparating conditions. The cold and hot eigenvalues were extrapolated to an infinite numbar of triangles per hex, i.e., as the triangle side length approaches zero. This was done for the mesh corner calculations and for the mesh center calculations using the method and equations discussed in Section 4.3.2, except that with only two points (6 and 24 triangles per hex), a linear (p =1.0) relationship had to be assumed. Since the mesh corner codes (BUGTRI, BUG 180, and GAUGE) gave essentially the sama k-eff in Table 4-3, the BUGTRI and GAUGE k-eff in Table 5-4 can be used together to maka such an extrapola-tion. The extrapolated values are given in Table 5-4 together with

-their average. This extrapolation is graphically shown in Fig. 5-7.

The k-eft discrepancy between cold and hot conditions is very small (Ak = 0.0003), when the average extrapolated values for an infinite num-ber of triangles per hex are considered. This is much less than with six triangles per hex in either the mesh corner approximation (cold-to-hot Ak = 0.0021) or the mesh center approximation (cold-to-hot Ak =

-0.0019). Therefore, the cold-te-hot k-eff discrepancy in the GAUGE calculations seems to be due to the use of a small number of mesh points in the finite difference approximation to the diffusion equation. The cold-to-hot k-eff discrepancy decreases as more triangles per hex are used in finite difference calculations. Th5 cold-to-hot k-eff dis-crepancy (Ak) approaches zero from the positive side for mesh corner codes, and approaches zero from the negative side for mesh center codes.

For purposes of the nodal DIF3D validation, it is significant that the nodal DIF3D calculation, with only one node per hex, obtains cold and hot eigenvalues which are vety close to the average extrapolated 5-20 e

909436 N/C Fig. 5-7 Extrapolation of 2-D Results to Zero Triangle Size COLD CRITICAL CONDITION (TP 640)

. 1.014 .:,,veren anemos.

....y.

• MESE CCENER 1.013 a j urns Cervan

1. _ _ . . - - i NODAL 1.010= g- _ . . . . -

.......y- - --

K O 1.008 1.006 1.004 . -

c-HOT OPERATING CONDITION (TP 650) 1.014 errrosion anemos.

.Y....

, ut3N CCRNEA

,, i s 1.012 ,,,.. - c_

.. ,,,.- ut$N CENTER

.- O

.-X~~~',,. NODAL 1.010 -

a K o ,

1.008

. 1 006 l 1.004 0.0 0.2 0.4 0.6 0.8 1.0 RELATIVE TRIANGLE SIZE y ,

TRIANGLES

• 96 54 24 6 PER HEX 5-21

909436 N/C values, closer than 24 triangles per hex either in mesh corner or mesh

. , , center codes. The cold-to-hot k-off discrepancy calculated by the nodal DIF3D code'is only-Ak = -0.0002. . This data indicates that the nodal DIF3D code appears to do a better calculation of k-eff than other codes for 2-D HTGR calculations.- Since the 3-D GATT code uses the same solu-

' tion techniques as the 2-D GADGE code, the nodal DIF3D code should also do a-better 3-D calculation of k-off than the GATT code. This conclu-sion is also supported.by data from the 3-D SNR-300 calculations in 4

~ Table 4-1, from the HTGR benchmark calculations in Table 4-2, and from the small HTGR core calculations in Table 4-3.

5.3.2. 3-D Reactivity Comparison The sigenvalues calculated in 3-D calculatione for the 170.4 to

+

,. 294.5 EFPD period of FSV Cycle 3 are listed in Table 5-6. The GATT values were obtained in previous fuel accountability calculations. The k-eff values calculated by the 3-D nodal DAF3D are close to'the GATT la values, being an average of caly Ak = -0.0013 different, with no Ak trend discernible. The DIFJD values being less than the GATT values bring them into closer agreement eith the FSV reactivity during steady power operation, i.e., k =1.000. Therefore, the nodal DIF3D code seems to do a better job in calculating the FSV reactivity than the GATT code.

The average k-eff difference of the 3-D nodal DIF3D calculation from reactor operation is only Ak = 0.0039 over this 124.5 EFPD burnup, and the DIF3D h-eff approaches 1.0 as the end of Cycle 3 is approached.

These features can be seen in Fig. 5-8, which plots the data in Table 5-6 at the end of the burnup intervals. The data is fit with fourth-order polynomial least-squares curves in Fig. 5-8.

, 5.4. RADIAL EAKING FACTOR COMPARISCN 5.4.1. 2-D RPF Comparison The radial peaking factors (RPFs) calculated in the 2-D calcula-tions listed in. Table 5-4 are compared in Appendix A. In each figure, 5-22

I: _

~

4 909436 N/C

, TABLE 5-6 3-D CALCULATIONS FOR FSV CYCLE 3 Cycle / ~* ' DIF-0ATT Page in Time Point EFPD GATT Nodal DIF3D Lh Appendix B 3/20 170.4 1.0345 1.0345 0.0000 B-2 3/21 180.0 1.0056 1.0056 0.0000 B-3 3/22 180.0 1.0198 1.0179 -0.0019 B-4 3/23 200.0 1.0040 1.0026 -0.0014 B-5 3/24 200.0 1.0159 1.0140 -0.0019 B-6 3/25 221.0 1.0099 1.0084 -0.0015 B-7 4 -

3/26 221.0 1.0097 1.0083 -0.0014 B-8 3/27 247.5 1.0038 1.0026 -0.0012 B-9

, , 3/28 247.5 1.0092 1.0080 -0.0012 B-10 3/29 268.2 1.0059 1.0046 -0.0013 B-11 3/30 282.7 1.0037 1.0027 -0.001z B-12 3/31 282.7 1.0037 1.0020 -0.0017 B-13 3/32 294.5 1.0026 1.0009 -0.0017 B-14 Average: 1.0051(a) 1,oo39(a) .o,0013 Deviation (la): *0.024(a) *0.0025(*) *0.0006

(*) Calculated for end of burnup interval values, since the control rods in the calculations were positioned during the interval to simulate the actual end of interval positions.

t I

4 5-23

.. . .=

.,- .~ . .,

Fig. 5-8. ,

K-EFF CALCULATED BY'3D CODES, 4 GROUPS 1.010 '^ CALCULATED K-EFF i

X O GATT 1.008 NODAL DIF3D e w E

I

/

- X O 1.006 ) %,/ /'~~

N -\ 7

/ N x ' ~ N V '-

N L

A v

^

\ '

L 1.004 X N 'N U \

E

\ O o o N X

\

1.002 Nx 0

1.000 s 180 200 220 240 260 280 300 b TIME (EFPD) IN CYCLE 3 A

909436 N/C the RPFs are given for the 37 regions in the FSV core. The upper-left

,. core diagram shows the reference RPF distribution. The upper-right core l diagram showr. the RPF distribution being compared to the reference values. The lower-right core diagram gives the percentage difference between the upper-right and the upper-left diagrams. In the lower left is a rtatistic.a1 analysis of the percent difference diagram in the lower-right. This is very useful to determine how well the two sets of l

RPF data compare. For example, the lower the one sigma deviation I l

between the two sets of RPF data for regions 1 through 37, the more similar are the two sets of RPF data.

.For>a set of values,,X i , the one sigma standard deviation is defined as

~"

f N

'.- f[ (Xi - m)2

, . p=1 ,

N

[Xi i=1 where m=

N is the mean of the Xi values, N= number of Xi values.

In this particular case, Xi = percent difference between RPFs for region i, N = 37 regions, and the mean of the percent difference should be close to zero due to cancellation of positive and negative percent difference values.

.' The averaga percent difference values for regions 1 through 19 and

. for regions 20 through 37 are a good indication of the invard/ outward power tilts. Local power tilts, i.e., toward the northwest section, would have to be appraised by considering the lower-right core diagram in Appendix A.

5-25

r 909436 N/C These figures are summarized in Table 5-7. Many of the comparisons g, in Appendix A use code calculated RPFs for the reference values. The calculated reference RPFs usually came from BUGTRI, because it was believed to be the best calculation. This belief was based on BUGTRI's use of 24 triangles per hex and a mesh corner finite difference approxi-mation to diffusion theory. Other comparisons in Appendix A use "GA-Measured" RPFs for the reference values for the hot core calculations at time point 650. These values are calculated at GA using the FSVCOR code (see Fig. 5-1) to analyze the measured data accumulated at FSV by the data logger. As explained in Section 5.2.2, GAUGE calculated RP."s are read into FSVCOR for regions 20 and 32 through 37, and are used .n the

+

core power normalization...Therefore, in Appendix A-12 through L-17, a true comparison between calculated and measured values is not * 'ng done for regions 20 and 32 through 37. It is not clear whether it wo21d be better to include or exclude these regions from the statistical aralysis of the percent RPF difference. For simplicity, these regions have been included in the statistical analysis in Appendix A-12 through A-17. No measured data is available at cold criticality. Therefore, the compari-son of measured and calculated results is not possible for the cold core at time point 640.

As indicated in Table 5-7, figures in Appendix A-2 through A-6 are based on calculations which used identical region cross sections (cold) appropriate for Cycle 3, time point 640 (Table 5-1). RPF differences between the various code results are therefore due to the inherent solu-tion methodology in the code, rather than on different data sets used.

The same cocid be said for figures on pages A-7 through A-11, except that these are based on hot cross sections for Cycle 3, time point 650.

Based on Table 5-7 and Appendix A, several conclusions can be made regarding the 2-D calculations.

• There is better agreement between calculations for a hot core (TP 650) than for a cold core (TP 640). This is probably t

because the hot core calculations have less than one-third as many rodded regions as the cold core calculations (Table 5-2).

5-26

g.. -

.- . 1 . . . .'.

TABLE 5-7

SUMMARY

OF RPF COMPARISONS FOR 2-D CALCULATIONS IN SEVEN GROUPS WITH AS-BUILT REFLECTOR IMPURITIES Calculation Average Percent Page in Time Reference Compared to Difference for One Sigma for . Appendix Point (a) Calculation Reference Regions 20-37 Regions 1-37 A 640 BUGTRI GAUGE 4.34 7.11 A-2 DIF3D, nodal -4.55 5.21 A-3 DIF3D, 6 T/ hex -4.66 5.69 A-4 DIF3D, 24 T/her -2.62 3.26 A-5 GAUGE DIF3D, nodal -8.02~ 11.30 A-6 650 BUGTRI GAUGE 2.58 3.85 A-7 DIF3D, nodal -3.09 3.85 A-8 DIF3D, 6 T/ hex -3.45 4.19 A-9 DIF3D, 24 T/ hex -1.87 2.64 A-10 GAUGE DIF3D, nodal -5.45 6.63 A-11

'GA measured" BUGTRI 7.22 9.49 A-12 GAUGE 9.87 11.44 A-13 DIF3D, nodal 3.92 7.71 A-14 DIF3D, 6 T/ hex 3.54 7.56 A-15 DIF3D, 24 T/ hex 5.19 8.13 A-16 "PSC measured" -0.55 1.65 A-17' (a)See Table 5-1.

i

?

E O

909436 N/C The power distribution calculated by the GAUGE code is higher g

,, .at the radial core-reflector interface than the reference BUGTRI calculation. The power distributions-calculated by the DIF3D code are lower at the radial core-reflector intetface than the reference BUGTRI calculation. This effect is appar--

ently due to the mesh corner versus mesh center diffusion approximation, as discussed for the small HTGR test problem (Section 4.3 and Table 4-4).

If more than 24 triangles per hex were used in the BUGTRI calculation, the radial power distribution weuld probably-shift toward the center of the core as it did in the small HTGR test problem (Table 4-4). This would bring it into better agreement with DIF3D code results.

c

• Relative to the BUGTRI power distributions, the nodal DIF3D is a better calculation than the 6 triangles / hex DIF3D, but not as good as the 24 triangles / hex DIF3D.

• The standard deviation of the region power differences between the GAUGE and nodal DIF3D codes is 6.6% (Appendix A-11) for the het core. The region powers calculated by these two codes are equally different from the reference BUGTRI (a = 3.85% in Appendices A-7 and A-8), except that the GAUGE powers are higher at the core edg.: (average percent difference for regions to through 37 - 2.58 in Appendix A-7), whereas the nodal DIF3D powers are lower at the core edge (average percent i

difference for regions 20 through 37 = -3.09 in Appendix A-8).

Therefore, the GAUGE and nodal DIF3D powers are cqually dif-ferent, though in opposite directions, from the reference

, BUGTRI powers.

I -

• Relative to the BUGTRI power distributions, the GAUGE powers are shifted toward the northwest sector of the core-reflector 5-28

909436 N/C boundary (Appendix A-7). The nodal DIF3D powers are shifted

, ,, away from the northwest sector of the core-reflector boundary (Appendix A-8). This appears to be due to the high k of the regions in this sector next to the reflector. I

]

The region RPF values calculated with GA's FSVCOR code from the FSV measurement data are compared to BUGTRI. GAUGE, and DIF3D results in Appendices A-12 through A-16. The signifi-cant discrepancies between the "measured" RPFs and the cal-culated RPFs indicate that the method of obtaining the "measured" RPFs is not as accurate as one would like, especially for regions 21 through 23.

To the extent that the "measured" RPFs are accurate, they are

, in better agreement with the nodal DIF3D powers than with the GAUGE powers. From Appendix A-14 the average percent differ-ence for regions 20 through 37 = 3.92, and the regions 1 through 37 a = 7.71 for the nodal DIF3D versus "measured" RPF comparison. From Appendix A-12 the average percent difference for regions 20 through 37 = 9.87, and the regions 1 through 37 a = 11.44 for the GAUGE versus "measured" RPF comparison.

• In Appendix A-17 the "measured" RPFs calculated from the FSV measurement data by GA with the FSVCOR code and by PSC with the POKE code are in good agreement. The differences that do exist indicate the effect of the approximations that are made in the two methods.

Several of these conclusions regarding the 2-D GAUGE / nodal DIF3D comparison will also be true for the 3-D GATT/ nodal DIF3D comparison in

the next section.

5-29

-.L

+ 9Q

v. 9@, 4g', IMAGE EVALUATION 40 9

% 4

,,,,,-.,< , . /////

V>;,, 4 l.0 l9MA[B G

u ru un t=

g, I.I $ I*

Ib ijil I.8 lal==

l.25 I l.4 pl I.6 1 ill =

• 150mm >

4 6" >

1

, 3,

• x o

l +(& +

m n,d

909436 N/C 5.4.2. 3-D RPF Comparison

.~

The radial peaking factors (RPFs) calculated in the 3-D calcula-tions listed in Table 5-6 are given in Appendix B. As listed in Table 5-8, B-2 to B-14 compare the GATT calculated RPFs to the nodal DIF3D calculated RPFs for time points 3/20 to 3/32. This time point designation, i.e., 3/20, refers to the cycle number (3), and the 3-D calculation number within the cycle (20). B-15 to B-21 compare the GATT calculated RPFs to the "measured" RPFs at the end of the burnup inter-vals. Comparisons are made only at the end of the burnup interval, because the control rod positione used in the calculations over each burnup interval corresponded to the actual control rod positions at the end of each interval. B-22 to B-28 compare the nodal DIF3D calculated RPFs to the "measured" RPFs at the end of the burnup intervals.

Table 5-8 summarizes the RPF results for the 3-D calculations.

Since the GATT and nodal DIF3D calculations used macroscopic cross ,

1 sections based on the same temperature dependent microscopic cross see-tion data, and on essentially the same temperatures, differences between the GATT and nodal DIF3D results will be due to differences between the solution methodologies of the codes. Based on Table 5-8, and Appen-olx B-2 to B-28, several conclusions can be drawn regarding the 3-D alculations.

• The largest percent difference between the GATT and nodal DIF3D RPFs was at the beginning of the 124 effective full power day (EFPD) burnup (3/20) where 0 = 7.17 for all the regions in the core. (This value is similar to the 0 = 6.6 for the GAUGE / nodal DIF3D 2-D comparison in Table 5-7.) This decreased to O = 3.53 at the end of the burnup (3/32) due to the effects of burnup; i.e., the regions with higher RPFs at the start of the burnup would deplete faster. The time dependence of the standard deviation of the percent RPF dif-ference is given in Fig. 5-9.

l l

l 5-30

Fig. 5-9.

DIFFERENCE BETWEEN GATT AND NODAL DIF3D RPFS 8

~

X S X I

N O N\ n

/\

D A _ _

R ^

D  %

Y ^N y 4 s, M p E

V _

X I

A T 2 I

O N -

O i i i i i i i g C

160 180 200 220 240 260 280 300 *

, z TIME (EFPD) IN CYCLE 3 E Y-AIIS IS STANDARD DEVI ATION OF % DIFFERENCE BETWEEN RPFS F OR ALL 37 REGIONS OF THE FSV CORE RPF - RADIAL PEAKING FACTOR DIFVAL* FIGS.CODEI

TABLE 5-8

SUMMARY

OF RPF COMPARISONS FOR 3-D CALCULATIONS Calculation Average Percent Page in -

Reference Compared to Cycle / Difference for One Signs for Appendix Powers Reference Time Point EFPD. Regions 20-37 Regions 1-37 'B GATT Nodal DIF3D 3/20 170.4. -5.14 7.17 B-2 3/21 180.0 -4.20 3.02 B-3 3/22 180.0 -4.10 6.84 B-4 3/23 200.0 -4.08 5.89 B-5 3/24 200.0 -3.52 5.72 B-6 3/25 221.0 -3.39 4.38 B-7 3/26 221.0 -3.57 4.47 B-8 3/27 247.5 -3.62 4.80 B-9 3/28 247.5 -3.62 4.86 B-10 3/29 268.2 -3.16 3.98 B-11 3/30 282.7 -3.13 3.97 B-12 7 3/31 282.7 -2.76 3.72 B-13

$ 3/32 294.5 -2.71 3.53 B-14 "Heasured" GATT 3/21 180.0 9.98 11.06 B-15 3/23 200.0 7.64 8.66 B-16 3/25 221.0 5.21 6.77 B-17 3/27 247.5 7.39 7.91 B-18 3/29 268.2 6.10 7.32 B-19 3/30 282.7 7.31 8.91 B-20 3/32 294.5 7.08 8.55 B-21

' Measured" Nodal DIF3D 3/21 180.0 5.50 9.10 B-22 3/23 200.0 3.19 5.56 B-23 3/25 221.0 1.67 5.21 B-24 3/27 247.5 3.46 4.51 B-25 3/29 268.2 2.78 5.54 B-26 $

3/30 282.7 3.96 6.50 B-27 51 3/32 294.5 4.22 6.85 B-28 $

E O

909436 N/C The curve is a fourth-order polynomial least-squares fit to

,, the data listed in Table 5-8, and shows the decreasing dif-farence between the GATT and nodal DIF3D RPFs. A deviation of 3% or 4% between the GATT and nodal DIF3D RPFs should be acceptable for FSV fuel accountability calculations. These results indicate that if the burnup with the DIF3D model started with the initial core, the differences between the GATT and nodal DIF3D RPFs by the beginning of Cycle 4 would have been even smaller.

Over the 124 EFPD burnup, the nodal DIF3D RPFs are closer to the "measured" values than the GATT RPFs. Figure 5-10 plots the standard deviation of the percent difference between the calculated and "measured" RPFs listed in Table 5-8 as a func-tion of time. The curves are fourth-order polynomial least-squares fits to the data. It shows that, to the extent that the "measured" values are correct, the nodal DIF3D code and model produce RPFs that are closer to reality than the GATT code. This is similar to the 2-D results from the nodal DIF3D and GAUGE calculations compared to the "measured" values (a =

11.4 for GAUGE, and a = 7.7 for the nodal DIF3D in Table 5-7).

Table 5-8 shows that the average percent difference between the nodal DIF3D RPFs and the GATT RPFs for regions 20 through 37 is negative, indicating that the RPFs calculated for the outer core regions next to the reflector are systematically lower in the nodal DIF3D calculation than in the GATT calcu-lation. This difference decreases from 5.1% at the beginning of the burnup (3/20) to 2.7% after 124 EFPD burnup (3/32).

This radial power shift with burnup is shown in Fig. 5-11.

, The differences between the nodal DIF3D and the GATT calcula-tions become less significant as burnup continues.

5-33 i

s Fig. 5-10.

DIFFERENCE BETWEEN CALCULATED AND MEASURED RPFS 12 S ,,m m ,,y,,,,,,

\ / \/

7 A S _

GATT VS MEAS.

T 10.0 A _ +-

y DIF3D VS MEAS.

D -

'N M

A R 7.5

\ q

\ x y X , / ~'

x ,

D -

N g ,g

\ O'

, y D

_ N -

w E

- "x N '

V S.O

's_ o ,

_g I _

A _

t T _

I 2.S O -

N -

o 0.0 i i i i i 3 180 200 220 240 260 280 300 g TIME (EFPD) IN CYCLE 3 Y-AIIS IS STANDARD DEVI ATION OF % DIFFERENCE BETWEEN RPFS F OR ALL 37 REGIONS OF THE FSV CORE RPF - RADIAL PEAKING FACTOR. 3-D CALCS. USING GATT F DIF3D CODES DIFVAL* FIGS. MEAS 2

, . ., .. .t' Fig. 5-11.

RADIAL POWER DISTRIBUTION DIFFERENCE. GATT VS. NODAL DIF3D V 70

_ s DIF. IN RPF E -

R -

v v ^

A O'O , N <> REGIONS I - is

'W G

E y

~

"rk -X REGIONS 20 - 37 P

2.5 E -

R -

C _

E 0.0 Y' N -

O T -

1

D -2.S I -

' 'X s - -

)V _ -t,-4 F _

y _

^

E R

-S.0 -

X' E _

N -

o C -7.S i i i i i i y E

• 160 180 200 220 240 260 280 300 w TIME (EFPD) IN CYCLE 3 3-D CALCULATIONS OF FSV USING GATT Er DIF3D CODES  % DIF. - (DIF3D RPF/GATT RPF - I)* LOO RPF - RADIAL PEAKING FACTOR DIFVAL* FIGS. CODE

909436 N/C

( -*

The 3-D RPF comparison is consistent with the 2-D RPF compari-

,, son. The average percent difference for regions 20 through 37 at 3/20 in the 3-D comparison (Table 5-8) is -5.14%. The

,' value for the 2-D RPF comparison (Tabic 5-6) between the nodal DIF3D and the GAUGE calculations is -5.45%.

Table 5-8 also shows that the RPFs for regions 20 through 37 calculated by the nodal DIF3D are in better agreement with the "measured" values than the RPFs calculated with GATT. This data is plotted in Fig. 5-12, which shows that the nodal DIF3D calculations give consistently closer results to the "mea-sured" values than the GATT calculations in this aspect of the RPF comparison.

As in the 2-D RPF comparison (Appendix A-11), there is also a larger RPF difference in the northwest sector of the 3-D RPF comparison. In Appendix B-2 for 3/20, the RPF difference for region 35 is -16%. This difference decreases rapidly over the next 30 EFPD to -7% as burnup begins and xenon builds in. The cause of this northwest sector difference is probably related to the fact that the highest core region k-infinities next to the reflector are also located in the northwest sector of the core at time point 3/20 (Fig. 5-13). If there were going to be differences in the calculated RPFs betvsen a mesh corner code, such as GAUGE or GATT, and a mech center code, such as DIF3D, the RPF differences would probably be largest where there was the largest difference betwean the k-infinities for two adjacent regions. The largest km difference in Fig. 5-13 occurs at the interface between region 35 (k. = 1.22) and the

,' reflector (k = 0.0). This is where the calculated RPFs are

, moct different in Appendices A-11 and B-2.  !

5-36

Fig. 5-12.

DIFFERENCE BETWEEN CALCULATED AND MEASURED RPFs 12 s nIF. IN Rer A X V ATT EEGIONS20-37 E 10 Y R -

DIF REGIONS 20-37 A

G E

\X y y v

n y-w 6

'N - y D c I - N p N F 4 x _ a E \ O '-

' '- u R -

\[]

N '-

N ' O E N %_

N 2 C o E -

0 i i i i i i 180 200 220 240 260 280 300 y TIME (EFPD) IN CYCLE 3 "

zo 3D CALCULATIONS OF FSV USING DIF3D F GATT  % DIF. - (CALC / MEAS - 1)'100 RADIAL PEAKING FACTORS (RPF) AVERAGED OVER REGIONS 20-37

909436 N/C Figure 5-13.

Region K-infinite, from

,, GAUGE calculation for Cycle 3, 170.4 EFPD ss S to 1.21 1.16 1.16 3, ss a

1.22 l' l.03 1.18  :

9 .93

.97 $

1.18 #

1.13 17

.92 33 1.10 to ss 1.10 3

.99 3

.17

. .94 5 1.08 1.07 i

• I' 22 l'

.96 11 1.13 1.10 4 1,17

.23 .93 is si 1.18 23 1.18 in 1.00 33 1.16 1.21 1.13 30 .88 #*

1.01 1.16 ,,

1.16 2,

2' .98 1.13 1.22 e

5-38

9094.'6 N/C i l

l 5.5. AXIAL PEAKING FACTOR COMPARISON I Use of the nodal DIF3D code, rather than the GATT code, should a

be expected to result in slightly different axial power distributions, l

Just as it resulted is slightly different radial power distributions. ,

Table 5-9 lists the axial peaking factors (APF) calculated by GATT at l l

3/21, which is the end of the first burnup interval. The number of axial elements which contain an inserted control rod is also given.

"Block 1" is the fuel element at the top of the core, and "block 6" is the fuel element at the bottom of the core. Table 5-10 gives the APFs froa the nodal DIF3D calculations at the same time point, 3/21.

In general, the APFs from the GATT and nodal DIF3D calculations are in good agreement. However, the axial power distribution of the nodal DIF3D calculation is shifted slightly to the top in the center of the core, and to the bottom in the outer radial regions of the core, relative t. the axial power distribution of the GATT calculation. The DIF3D/GATT ratios of the top block APF for each ring are as follows ct time point 3/21: 1.029 for region 1; 1.012 for regions 2 to 73 0.994 for regions 8 to 191 and 0.984 for regions 20 to 37. The ratio for all core regions is 0.993, indicating overall agreement within 1%.

In Table 5-11, the power fractions in the top half of the core cal-culated by GATT and DIF3D indicate very little change in the axial power distribution differences over the 124 EFPD burnup. In Table 5-12, some change can be noted. The bottom layer APF for region 1 at 180.0 EFPD is 2.5% lower when calculated by DIF3D when calculated by GATT. Over the 124 EFPD burnup, this reduces to a 1.9% difference.

These small differences in the axial power distribution between the GATT and the nodal DIF3D calculations are acceptable. Accurate compari-sons between calculated and measured axial power distributions are not available due to the lack of good measured data.

5-39

. .. . o .

TABLE 5-9 GATT RESULTS AXIAL POWER PROFILES FOR CYCLE 3 AT 188.8 EFPD ROD RECT *W INSERTION BLOCK 1 BLOCK 2 BLOCK 3 BLOCK 4 BLOCK 5 RLOCK 6 1 2 .628 .924 1.295 1.276 1.112 .765 2 e .817 1.141 1.285 1.996 .977 .683 3 e .769 1.986 1.287 1.132 .995 .738 4 e .818 1.183 1.386 1.076 .936 .639 5 e .797 1.153 1.385 1.862 .928 .675 6 8 .827 1.12s 1.271 1.186 .983 .693 7 8 .793 1.878 1.267 1.133 1.915 .714 8 e .905 1.278 1.335 1.818 .834 .579 9 8 .858 1.898 1.258 1.121 .973 .699 18 2 .668 .932 1.397 1.199 1.849 .754 11 6 .827 1.148 1.388 1.121 .953 .658 12 8 .898 1.215 1.283 1.987 .968 .625 13 6 .843 1.186 1.295 1.123 .947 .686 14 2 .631 .898 1.282 1.289 1.113 .795 15 6 .839 1.176 1.388 1.954 .899 .653 I"

b 16 s .868 1.2e6 1.383 1.884 .916 .638 C'

17 6 .897 1.172 1.369 1.822 .888 .652 18 2 .643 .923 1.334 1.262 1.066 .752 19 6 .857 1.159 1.277 1.188 .943 .656 26 8 .925 1.216 1.268 1.981 .905 .613 21 6 .972 1.250 1.378 .986 .828 .586 22 8 .764 1.885 1.258 1.163 1.8 3 .717 23 8 .757 1.842 1.226 1.179 1.866 .748 24 0 .831 1.117 1.243 1.127 .988 .694 25 8 .936 1.387 1.419 .999 .864 .535 26 8 .918 1.225 1.277 1.984 .897 .600 27 6 .961 1.176 1.214 1.972 .923 .654 28 8 .787 1.149 1.372 1.984 .943 .664 29 8 .736 1.057 1.268 1.182 1.836 .729 as 8 .798 1.999 1.217 1.145 1.814 .732 31 8 .8E2 1.169 1.253 1.082 .944 .678 32 8 .942 1.318 1.'424 .983 .797 .536 33 6 .925 1.195 1.277 1.871 .895 .637 34 e .864 1.118 1.268 1.141 .986 .686 35 8 .802 1.168 1.386 1.898 .926 .626 36 8 .855 1.245 1.441 1.004 .849 .557 37 8 .892 1.215 1.284 1.889 .908 .628 AVERAGE .828 1.137 1.311 1.168 .949 .667 SUM e

o e

b u

0%

Z O

TABLE 5-10 DIF3D RESULTS - CYCLE 3, 180.0 EFPD APFS FOR FSV CORE REGIONS (LEVEL 1 IS TOP LEVEL 6 IS BOTTO'J)

REGION NO. LEVEL 1 LEVEL 2 LEVEL 3 LEVEL 4 LEVEL 5 LEVEL 6 1 S.646 S.958 1.382 1.259 1.889 S.746 2 S.826 1.166 1.285 1.887 8.964 S.671 3 S.782 1.115 1.288 1.122 S.988 S.714 l 4 8.813 1.286 1.381 1.074 S.897 S.628 1 5 S.885 1.181 1.383 1.856 S.916 S.661 l 6 S.838 1.147 1.273 1.996 S.968 S.879 7 8.886 1.196 1.268 1.121 S.999 S.758 8 S.888 1.283 1.392 1.524 8.836 S.577 S 8.859 1.121 1.254 1.115 S.964 S.688 18 S.663 S.951 1.397 1.281 1.843 S.745 11 S.823 1.159 1.382 1.117 S.948 S.651 12 8.879 1.228 1.284 1.986 S.988 S.623 13 f.844 1.128 1.297 1.117 S.939 S.675 14 S.638 S.916 1.298 1.278 1.898 S.788 15 S.833 1.192 1.377 1.857 S.897 S.644 16 S.852 1.216 1.383 1.882 S.913 S.634 17 0.898 1.189 1.363 1.026 S.887 S.645 en 18 S.663 S.943 1.334 1.255 1.868 S.745 s 19 8.852 1.177 1.278 1.184 S.939 S.668 j[ 28 8.983 1.224 1.263 1.985 S.989 S.616 21 S.948 1.261 1.367 S.998 S.837 S.589 22 8.768 1.897 1.253 1.163 1.812 8.715 23 S.742 1.858 1.229 1.182 1.857 S.741 24 S.828 1.122 1.243 1.129 S.998 S.698 25 S.917 1.383 1.485 1.812 S.818 S.545 26 S.095 1.229 1.275 1.887 5.985 S.689 27 8.945 1.188 1.215 1.874 S.928 S.658 28 S.779 1.153 1.362 1.891 S.949 8.667 29 S.725 1.866 1.258 1.183 1.838 8.738 38 S.795 1.188 1.218 1.139 1.811 S.729 31 S.875 1.177 1.252 1.881 S.945 S.678 32 8.923 1.317 1.486 8.995 S.812 S.547 33 S.912 1.199 1.274 1.873 S.982 S.641 34 S.797 1.124 1.263 1.141 8.988 8.689 35 S.779 1.165 1.375 1.118 S.948 S.638 36 S.838 1.248 1.426 1.065 S.863 S.568 37 8.888 1.228 1.282 1.898 S.983 S.624 CORE AVE S.822 1.151 1.389 1.187 S.947 S.664 e

O e

k ta 0%

• 4 O

TABLE 5-11

SUMMARY

OF CONTROL ROD INSERTIONS AND POWER FRACTION IN TOF HALF OF CORE 180.0 EFPD 200.2 EFPD 220.8 EFPD 247.5 EFPD 268.2 EFPD 282.7 EFPD 294.5 EFPD CR GATT DIF CR GATT DIF CR GATT DIF CR GATT DIF CR GATT DIF CR GATT DIF CR GATT DIFF 1 2 .475 .484 2 .499 .504 2 .456 .466 2 .455 .464 2 .462 .471 2 .462 .472 2 .464 .473 2 0 .541 .546 0 .561 .561 0 .509 .516 0 .509 .513 0 .515 .521 0 .516 .521 0 .518 ,523 3 0 .524 .53" 0 .562 .562 0 .506 .513 0 .506 .511 0 .513 .520 0 .514 .520 0 .516 .522 4 0 .563 .567 0 .585 .584 0 .530 .536 0 .531 .535 0 .539 .543 0 .540 .545 0 -.543 .543 5 0 .556 .561 0 .592 .592 0 .537 .543 0 .538 .542 0 .546 .551 0 .548 .553 0 .550 .556 6 0 .536 .543 0 .559 .561 0 .502 510 0 .501 .5P7 0 .508 .515 0 .509 .516 0 .511 .518 7 0 .523 .530 0 .561 .561 0 .504 .111 0 .504 .501 0 .511 .517 0 .512 .517 0 .514 .519 8 0 .595 .594 0 .590 .588 0 .558 .558 0 .557 .555 0 .561 .562 0 .562 .562 0 .564 .564 9 6 .535 .539 6 .559 .559 6 .540 .541 6 .540 .538 6 .543 .543 6 .544 .543 6 .543 .545 10 2 .500 502 0 .603 .596 0 .551 .553 0 .552 .552 0 .558 .560 0 .560 .561 0 .563 .564 11 6 .545 .547 6 .576 .573 3 .441 .452 3 .442 .451 2 .466 .475 2 .467 .476 2 .472 .478 12 0 .565 .565 0 .563 .562 0 .521 .523 0 .520 .521 0 .524 .526 0 .525 .527 0 .527 .530 13 6 .541 .545 6 .568 .567 6 .541 .543 6 .542 .540 6 .545 .544 6 .546 .546 6 .545 .548 14 2 .467 .474 0 .571 .569 0 .516 .520 0 .514 .516 0 .519 .522 0 .520 .523 0 .522 .526 15 6 .566 .567 6 .601 .598 3 .461 .469 3 .460 .466 e .484 .491 2 .486 .492 2 .490 .494 m 16 0 .560 .561 0 .561 .563 0 .516 .520 0 .514 .515 0 .519 .521 0 .520 .522 0 .522 .524 L 17 6 .573 .574 6 .602 .599 6 .576 .574 6 .576 .571 6 .579 .576 6 .580 .576 6 .580 .579

" .487 .584 .537 .539 18 2 .490 0 .579 0 .534 .534 3 .533 .532 0 .537 0 .538 .538 0 .540 19 6 .549 .551 6 .578 .575 3 .448 .456 3 .449 .456 2 .470 .477 2 .471 .478 2 .476 .480 20 0 .567 .565 0 .547 .546 0 .538 .536 0 .537 .532 0 .538 .536 0 .539 .536 0 .540 .539 21 6 .600 .596 1 .556 .556 0 .586 .581 0 .585 .579 0 .587 .583 0 .587 .583 0 .589 .586 22 0 .518 .518 0 .552 .549 0 .547 .545 0 .544 .541 4 .546 .545 0 .546 .545 0 .546 .546 23 0 .504 .503 0 .562 .556 0 .529 .528 0 .527 .526 0 .529 531 0 .530 .531 0 .532 .531 24 0 .532 .531 0 .571 .567 0 .511 .512 0 .509 .509 0 .515 .517 0 .516 .518 0 .519 .520 25 0 .610 .604 0 .618 .610 0 .563 .559 0 .562 .558 0 .56o .564 0 .569 .565 0 .572 .568 26 0 .570 .566 0 .554 .551 0 .535 .533 0 .533 .531 0 .535 .533 0 .535 .534 0 .537 .535 27 6 .558 .557 1 .519 .521 0 .543 .542 0 .540 .538 0 .541 .540 0 .541 .541 0 .543 .542 28 0 .551 .549 0 .586 .581 0 .576 .572 0 .574 .569 0 .576 .572 0 .577 .574 0 .579 .575 29 0 .509 .508 0 .566 .561 0 .533 .531 0 .530 .527 0 .532 .530 0 .532 .531 0 .534 .532 30 0 .519 .520 0 .563 .561 0 .496 .498 0 .493 .494 0 .500 .501 0 .500 .502 0 .502 .503 31 0 .551 .551 0 .560 .560 0 .501 .502 0 .497 .497 0 .503 .504 0 .503 .505 0 .506 .506 32 0 .614 .608 0 .604 .600 0 .585 .579 0 .581 .573 0 .583 .577 0 .584 .578 0 .586 .580 33 6 .566 .564 1 .532 .536 0 .551 .550 0 .547 .544 0 .548 .547 0 .548 .547 0 .549 .548 34 0 .531 .531 0 .565 .552 0 .553 .550 0 .548 .545 0 .549 .547 0 .549 .547 0 .551 .549 35 0 .559 .553 0 .604 .596 0 .576 .569 0 .'75 .567 0 .576 .571 0 .577 .571 0 .578 .573 $

36 0 .590 .584 0 .625 .615 0 .572 .565 0 .572 .563 0- .575 .569 0 .576 .569 0 .579 .573 $

37 0 .565 .564 0 .569 .566 0 .520 .518 0 .519 .515 0 .523 .521 0 .523 .521 0 .526 .524 $

z AVERAGE .546 .547 .571 .569 .528 .529 .527 .526 .532 .534 .533 .534 .535 .536 2i '

. s TABLE 5-12

SUMMARY

OF CONTROL ROD INSERTIONS AND AXIAL POWER FACTORS IN BOTTOM LAYER 180.0 EFPD ,_

200.2 EFPD 220.8 EFPD 247.5 EFPD 268.2 EPPD 282.7 EFPD 294.5 EFPD CR GATT DIF CR GATT DIF CR CATT DIF CR CATT DIF CR CATT DIF CR CATT DIF CR GATT DIF *A 1 2 .765 .746 2 .727 .720 2 .858 .835 2 .869 .850 2 .837 .819 2 .839 .822 7. .838 .822 -1.9 2 0 .683 .671 0 .650 .652 0 .794 .776 0 .803 .792 0 .766 .754 0 .767 .758 0 .765 .735 -1.3 3 0 .730 .714 0 .666 .667 0 .823 .802 0 .831 .816 0 .790 .776 0 .790 .778 0 .788 .776 -1.5 4 0 .639 .628 0 .607 .606 0 .756 .738 0 .763 .750 0 .726 .715 0 .726 .716 0 .724 .713 - 1. 5 ~

5 0 .675 .661 0 .617 .616 0 .771 .753 0 .780 .767 0 .740 .729 0 .741 .730 0 .738 .727 -1.5 f 6 0 .693 .679 0 .657 .653 0 .813 .794 0 .823 .811 0 .782 .770 0 .783 .772 0 .781 .770 -1.4 7 0 .714 .700 0 .652 .653 0 .806 .789 0 .815 .803 0 .776 .765 0 .778 .768 0 ,776 .767 -1.2 8 0 .579 .577 0 .588 .592 0 .690 .683 0 .702 .701 0 .678 .672 0 .679 .677 0 .678 .675 -0.4 9 6 .699 .688 6 .651 .654 6 .725 .723 6 .738 .741 6 .720 .718 6 .721 .723 6 .726 .720 -0.S 10 2 .754 .745 0 .587 .599 0 .731 .721 0 .741 .737 0 .709 .702 0 .710 .705 0 .707 .704 -0.4 11 6 .658 .651 6 .609 .614 3 .923 .894 3 .931 .908 2 .825 .805 2 .327 .809 2 .818 609 -1.1 12 0 .625 .623 0 .636 .639 0 .764 .754 0 .774 .769 0 .743 .739 0 .745 .741 0 .743 .738 -0.7 13 6 .686 .675 6 .642 .642 6 .728 .726 6 .740 .741 6 .720 .720 6 .721 .721 6 .725 5719 -0.8 14 2 .795 .780 0 .627 .633 0 .779 .767 0 .793 .786 0 .759 .751 0 .760 .753 0 .758 .751 -0.9 15 6 .653 .644 6 .594 .596 3 .913 .885 3 .926 .904 2 .814 .795 2 .815 .798 2 .808 .799 -1.1 w 16 0 .638 .634 0 .638 .636 0 .770 .761 0 .782 .781 0 .748 .744 0 .750 .747 0 .748 .745 -0.4 L 17 6 .652 .645 6 .602 .605 6 .687 .689 6 .699 .705 6 .681 .684 6 .682 .687 6 .686 .685 -0.1 18 2 .752 .745 0 .599 .611 0 .738 .734 0 1749 .750 0 .721 .719 0 .722 .723 0 .721 .719 -0.3 19 6 .656 .650 6 .610 .616 3 .913 .888 3 .922 .904 2 .822 .805 2 .825 .811 2 .817 .810 -0.9 20 0 .613 .616 0 .650 .656 0 .707 .709 0 .721 .729 0 .711 .713 0 .713 .719 0 .713 .716 0.4 21 6 .586 .589 1 .644 .644 0 .633 .637 0 .646 .656 0 .643 .646 0 .645 .652 0 .645 .650 G.8 22 0 .717 .715 0 .651 .660 0 .697 .699 0 .712 .719 0 .705 .705 0 .706 .710 0 .706 .708 0.3 23 0 .740 .741 0 .640 .652 0 .740 .739 0 .756 .755 0 .740 .735 0 .742 .739 0 .740 .741 0.1 24 0 .694 .696 0 .628 .639 0 .792 .787 0 .806 .804 0 .770 .765 0 .772 .768 0 .769 .768 -0.1 25 0 .535 .545 0 .528 .543 0 .672 .675 0 .682 .687 0 .652 .655 0 .654 .657 0 .652 .656 0.6 26 0 .600 .609 0 .638 .648 0 .713 .717 0 .)24 .730 0 .711 .714 0 .713 .716 0 .712 .717 0.7.

27 6 .654 .658 1 .716 .714 0 .718 .720 0 .733 .737 0 .727 .728 0 .729 .730 0 .728 .731 0.4 28 0 .664 .667 0 .607 .617 0 .660 .666 0 .677 .684 0 .671 .676 0 .673 .677 0 .671 .67/ 0.9 29 0 .729 .730 0 .629 .641 0 .730 .733 0 .745 .751 0 .730 .733 0 .732 .734 0 .730 .735 0.7 30 0 .732 .729 0 .654 .659 0 .833 .826 0 .848 .845 0 .805 .800 0 .806 .802 0 .805 .803 -0.3 31 0 .670 .470 0 .655 .658 0 .820 .815 0 .837 .837 0 .798 .794 0 .800 .797 0 .798 .797 -0.1 32 0 .536 .547 0 .554 .562 0 .624 .633 0 .639 .653 0 .626 .636 0 .628 .639. 0 .626 .636 1.6 33 6 .637 .641 1 .679 .674 0 .690 692 0 .708 .714 0 .700 .702 0 .701 .705 0 .701 .705 0.6 34 0 .686 .689 0 .630 .638 0 .687 .691 0 .707 .714 0 .701 .704 0 .703 .708 0 .703 .706 0.4 >

35 0 .620 .630 0 .551 .567 0 .637 .646 0 .652 .664 0 .644 .651 0 .647 .656 0 .648 .656 1.2 36 0 .551 .568 0 .506 .524 0 .643 .631 0 .654 .668 0 .630 .638 0 .633 .644 0 .632 .639 1.1 37 0 .620 .624 0 .622 .631 0 .763 .763 0 .775 .781 0 .746 .747 0 .749 .752 0 .747 .750 0.4 AVERAGE .667 .664 .626 .631 .753 .746 .765 .763 .733 .729 .735 .732 .733 .731 -0.3

909436 N/C l

5.6. FUEL ACCOUNTABILITY COMPARISON The GATT code is used primarily to calculate the 3-D burnup for the Fort St. Vrain reactor. For the nodal DIF3D code to achieve a validated status, it must be shown that it can also perform an acceptable burnup 1

calculation. Tables 5-13 through 5-23 relate to the GATT versus nodal  !

DIF3D burnup comparison.

Tables 5-13 and 5-14 give the fractional absorptions calculated by GATT and DIF3D. Fractional absorptions are generally within 1% between the two codes, except for the lumped burnable poison, where there is initially a 2.4% difference. The good agreement between the control rod fractional absorptions indicates that the same control rod shielding factors can be used in the nodal DIF3D cciculation as in the GATT calcu-lation. The DIF3D calculations gave lower core km and core leakage, which usually resulted in lower k-eff values. The DIF3D calculations also gave radial and axial components of the core leakage.

Tables 5-15 and 5-16 give the core loadings over the 124 EFPD burnup. Unfortunately, Avogadro's number used in DIF3D to calculate the nuclide weights from the region volumes and atom densities was 6.0222 x 1023 atoms /gm-mole, whereas 6.0238 x 1023 was used in the GATT calculational sequence in Cycle 3. Multiplying the GATT core loadings by the ratio 6.0238/6.0222 = 1.0002657 brings them into good agreement with :he core loadings calculated by DIF3D. For example, the fertile particle Th-232 decrease is only 1% different between the two codes.

The fissile particle U-235 burnup is about 0.4% different. Even though j the loadings for the entire core agree so closely in Tables ;-15 and 5-16, there are local burnup differences that result from the different l ,- radial and axial power distributions calculated in GATT and the nodal DIF3D. Some of these local burnup differences can be distinguished in Tables 5-17 to 5-19.

5-44

. , . t * . ..

TABLE 5-13 FRACTIONAL ABSORPTIONS - GATT EFPD: 180.0 200.0 221.0 247.5 268.2 282.7 294.5 Nuclide T.P.: 3/21 3/23 3/25 3/27 3/29 3/30 3/32 Th-232 .3110 .3172 .3223 .3230 .3246 .3250 .3255 Pa-233 .0016 .0038 .0038 .0056 .0059 .0061 .0061 U-233 .1778 .1783 .1833 .1886 .1951 .1987 .2018' U-234 .0023 .0024 .0024 .0025. .0026 .0026 .0026 U-235 ,.3390 .3367 .3327 .3234 .3156 .3103 .3062 U-236 .0072 .0076 .0077 .0081 .0083 .0085 .0086 U-238 .0041 .0042 .0042 .0042 .0042 .0043 .0042 -l Xe-135 .0159 .0186 .0187 .0189 .0190 .0190 .0188 Sm-149 .0048 .0052 .0053 .0054 .0054 .0055 .0055'

. LBP .0164 .0146 .0133 .0115 .0101 .0092 .0086 L Silicon .0097 .0097 .0101 .0101 .0102 .0102 .0103 Carbon .0132 .0132 .0138 .0138 .0139 .0140 .0140 Control Rod .0432 .0315 .0220 .0225 .0195 .0196 .0196 K-eff 1.0056 1.0040 1.0099 1.0038 1.0059 1.0037 1.0026 Ltotal .0605 .0627 .0625 .0629 .0611 .0614 .0616 K. 1.071 1.071 1.073 1.072 1.072 1.070' 1.069 i

l i

E o

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

TABLE 5-14 FRACTIONAL ABSORPTIONS - DIF3D EFPD: 180.0 200.0 221.0 247.5 268.2 282.7 294.5 Nuclide T.P.: 3/21 3/23 3/25 3/27 3/29 3/30 3/32 Th-232 .3133 .3196 .3244 .3246 .3262 .3265 .3273 Pa-233 .0017 .0039 .0049 .0056 .0060 .0061 .0061 U-233 .1788 .1788 .1836 .1889 .1955 .1990 .2019 U-234 .0023 .0024 .0024 .0025 .0026 .0026 .0027 U-235 .3356 .3342 .3300 .3211 .3133 .3083 .3040 U-236 .0073 .0076 .0078 .0081 .0084 .0086 .0087 U-238 .0041 .0043 .0042 .0042 .0042 .0042 .0042 Xe-135 .0158 .0185 .0186 .0189 .0189 .0189 .0187 Sm-149 .0047 .0051 .0053 .0054 .0054 .0054 .0054 LBP .0160 .0144 .0131 .0113 .0100 .0092 .0085 I Silicon .0007 .0097 .0101 .0101 .0101 .0102 .0102

$ Carbon .0132 .0132 .0138 .0138 .0139 .0140 .0140 Control Rod .0432 .0310 .0222 .0226 .0196 .0196 .0197 K-eff 1.0056 1.0026 1.0084 1.0026 1.0046 A,0025 1.0009 Leakage, radial .0364 .0388 .0380 .0381 .0375 .0375 .0376 axial .0204 .0208 .0221 .0224 .0217 .0219 .0220 total .0568 .0597 .0601 .0605 .0592 .0594 .0597 K. 1.0717 1.0690 1.0729 1.0677 1.0676 1.0659 1.0643 o

E o

TABLE 5-15 CORE LOADINGS - GATT (kg)

EFPD: 180.0 200.0 221.0 247.5 268.2 282.7 294.5 Nuclide T.P.: 3/21 3/23 3/25 3/27 3/29 3/30 3/32 Th-232 10,890.5 10,881.0 10,871.2 10,858.4 10,848.4 10,841.4 10,835.6 Pa-233 3.4 8.2 10.3 11.9 12.5 12.7 12.7 U-233 143.0 142.3 144.2 147.8 151.1 153.5 155.7 U-234 9.6 10.2 10.8 11.7 12.4 12.9 13.3 U-235 0.9 1.0 1.1 1.2 1.3 1.3 1.4 U-236 0.05 0.05 0.06 0.07 0.08 0.08 0.09 Pa-231 0.04 0.04 0.04 0.04 0.04 0.04 0.04 U-232 0.02 0.02 0.03 0.03 0.03 0.03 0.03 Th-232 3,691.9 3,688.6 3,685.3 3,680.9 3,677.4 3,675.0 3,673.0 Pa-233 1.2 2.8 3.5 4.1 4.3 4.4 4.4 y

• - U-233 48.0 47.9 48.6 49.9 51.1 51.9 52.7 I U-234 8.8 8.9 9.1 9.3 9.5 9.6 9.7 U-235 489.6 475.8 462.0 444.4 431.0 421.9 414.4 i U-236 75.3 77.7 80.0 82.9 85.1 86.6 87.8 U-238 52.0 51.9 51.7 51.5 51.3 51.2 51.1 Np-237 3.6 3.9 4.1 4.4 4.7 4.9 5.0 Np-239 0.01 0.02 0.02 0.02 0.02 0.02 0.02 Pu-238 0.59 0.65 0.71 0.80 0.87 0.92 0.96 Pu-239 1.22 1.23 1.2 1.3 1.3 1.3 1.3 Pu-240 0.36 0.37 0.38 0.40 0.41 0.41 0.42 Pu-241 0.31 0.33 0.35 0.37 0.39 0.40 0.41 Pu-242 0.11 0.12 0.14 0.15 0.16 0.17 0.18 Pa-231 0.01 0.01 0.01 0.01 0.01 0.01 0.01 U-232 0.01 0.01 0.01 0.01 0.01 0.01 0.01 Total 15,420.5 15,403.1 15,384.9 15,361.5 15,343.4 15,330.6 15,320.2

?

E a

.. .. .~.

TABLE 5-16 CORE LOADINGS - DIF3D (kg)

EFPD: 180.0 200.0 221.0 247.5 268.2 282.7 294.5 Nuclide T.P.: 3f21 3/23 3/25 3/27 3/29 3/30 3/32 Th-232 10,893.3 10,883.8 10,873.8 10,860.9 10,850.8 10,843.7 10,837.8 q Pa-233 3.5 8.2 10.5 12.0 12.6 12.8 12.8 U-233 143.0 142.3 144.3 148.0 151.3 153.8 156.0 U-234 9.6 10.2 10.8 11.7 12.4 12.9 13.3 U-235 0.9 1.0 1.0 1.2 1.3 1.4 1.4 U-236 .05 .05 .06 .07 .08 .08 .09 Pa-231 .04 .04 .04 .04 .04 .04 .04 U-232 .02 .02 .03 .03 .03 .03 .03 Th-232 3,692.9 3,689.5 3,686.2 3,681.7 3,678.2 3,675.8 3,673.8 ja Pa-233 1.2 2.9 3.6 4.1 4.3 4.4 4.4 g U-233 48.1 47.9 48.6 50.0 51.2 52.0 $2.8 U-234 8.3 8.9 9.1 9.3 9.5 9.6 9.7 U-235 489.7 476.1 462.2 444.7 431.4 422.3 ,414.8 U-236 75.4 77.7 80.0 82.9 85.1 86.6 87.8 U-238 52.1 51.9 51.7 51.5 51.3 51.2 51.1 Np-237 3.6 3.9 4.1 4.4 4.7 4.9 5.0 Np-239 0.01 0.02 0.02 0.02 0.02 0.02 0.02 Pu-238 0.59 0.65 0.71 0.80 0.87 0.92 ' O.96 Pu-239 1.22 1.23 1.24 1.26 1.27 1.28 1.28 Pu-240 0.36 0.37 0.38 0.40 0.41 0.41 0.42 Pu-241 0.31 0.33 0.35 0.37 0.39 0.40 0.41 Pu-242 0.11 0.12 0.14 0.15 0.16 0.17 0.18 Pa-231 0.01 0.01 0.01 0.01 0.01 0.01 0.01 U-232 0.01 0.01 0.01 0.01 0.01 0.01 0.01 Total 15,425.0 15,407.2 15,388.9 15,365.6 15,347.4 15,334.8 15,324.2 o

8:

E o

TABIJE 5-17 MAXIMUM FISSILE PARTICLE BURNUP AT 3/32 RESULTS FROM GATT CALCULATIONS ON UNIVAC FSV, CYCLE 3, 294.5 EFPD LAYER SEGMENT FIMA,5 BLOCK PATCH COLLASI EFPO FIMA,5 BLOCK PATCH COLUted EFPD 4 3 9.23 1-0065 3 7 657.3s 18.44 2-2424 3 1 657.38 4 4 9.49 1-1371 2 3 667.38 11.12 2-2096 2 1 657.38 4 5 9.39 1-1368 7 5 657.38 18.94 2-8244 7 1 667.34 4 6 9.26 1-8144 6 2 857.38 18.86 2-2413 6 1 657.38 4 7 6.64 5-5223 35 6 483.38 S.05 6-4587 35 1 483.38 l 4 8 4.98 E-5268 36 2 294.59 5.15 6-5422 32 1 294.58 '

S 3 11.78 1-9043 3 7 657.38 12.64 2-2263 3 1 667.38 )

5 4 11.94 1-8555 E 6 657.38 13.22 2-2661 2 1 667.34 5 5 12.83 1-8281 7 5 667.38 13.24 2-2236 7 1 657.38 5 6 11.97 1-1987 6 2 157.38 13.15 2-2739 6 1 457.38 5 7 9.28 5-4813 35 6 433.34 18.43 6-5716 35 1 483.38 5 8 6.95 5-4471 36 2 294.58 6.91 6-6406 32 1 294.58 6 3 12.84 1-8588 3 7 667.10 13.43 2-1519 3 1 667.38 6 4 13.18 1-1252 2 4 667.30 13.92 2-2863 2 1 667.38 gn 6 5 13.21 1-1454 7 4 667.38 13.94 2-1545 7 1 667.38 e 6 6 13.23 1-1710 6 3 667.38 13.91 2-0548 6 1 667.38 j$ 6 7 18.28 1-2285 6 7 483.38 11.88 2-6874 5 1 483.38 6 8 7.56 6-1474 36 2 294.58 7.35 2-4642 8 1 294.58 7 3 13.55 1-e924 3 7 657.38 13.73 2-8577 3 1 657.38 7 4 13.75 1-8977 2 4 667.38 14.82 2-2162 2 1 657.38 7 5 14.08 1-1672 1 7 667.38 14.14 2-2477 1 1 857.38 l 7 6 13.86 1-8257 6 3 667.38 14.01 2-1774 6 1 667.38 7 7 12.29 1-4815 6 7 483.38 12.62 2-4187 5 1 483.38 7 8 8.38 5-5856 36 2 294.58 S.39 2-5426 4 1 294.58 8 3 12.11 1-9888 3 7 667.38 11.96 2-1844 3 1 667.38 8 4 12.35 1-9894 2 7 667.38 12.23 2-2452 2 1 667.38 9 5 12.69 1-Seel 1 7 657.38 12.37 2-2761 1 1 667.38 0 6 12.44 1-2273 6 2 667.38 12.21 2-2694 6 1 657.38 8 7 11.21 1-4578 5 2 483.38 11.06 2-5786 5 1 483.38 8 8 7.16 1-5417 4 6 294.58 7.26 2-4589 4 1 294.58 9 3 9.39 1-8587 3 2 657.38 9.41 3-1766 3 1 667.38 9 4 9.70 1-8855 2 7 667.38 9.65 3-8886 2 1 667.38 9 5 9.97 1-2828 1 7 857.38 9.79 3-1998 1 1 667.38 9 6 9.73 1-1193 6 2 667.3e 9.64 3-2421 6 1 657.38 9 7 8.64 1-8519 5 2 483.30 8.55 3-4146 5 1 483.38 9 8 5.43 1-5259 4 2 294.55 5.56 3-1432 4 1 294.58 e

C.

a

. . . i . . . .

TABLE 5-18 MAXIMUM FISSILE PARTICLE BURNUP AT 3/32 RESULTS FROW DIF3D CALCULATIONS ON CRAY FSV, CYCLE 3, 294.5 EFPO LAYER SEGMENT FIWA,3 SLOCK PATCH COLLAsd EFPD FIWA,5 SLOCK PATCH COLLAsd EFfD 4 3 9.33 18665 3 7 667.3e 18.57 22424 3 1 667.39 4 4 9.57 1-1371 2 3 667.38 11.22 2-209e 2 1 657.34 4 5 9.47 1-1368 7 5 667.38 11.e4 2-8244 7 1 667.38 4 6 9.35 1-e144 6 2 667.38 18.98 2-2413 6 1 667.Se 4 7 6.43 E-5223 36 6 483.3e 8.13 6-4E87 35 1 483.38 4 8 4.74 6-626e 36 2 294.58 E.27 6-5422 32 1 294.58 5 3 11.78 18843 3 7 657.Se 12.71 22263 3 1 857.38 5 4 12.81 1-8655 2 6 667.3e 13.31 2-2661 2 1 667.3e 5 5 12.18 1-8281 7 5 657.3e 13.32 2-2236 7 1 657.38 5 6 12.85 1-19e7 6 2 667.38 13.26 2-2739 6 1 657.39 5 7 8.96 E-6864 21 3 483.38 18.23 6-5716 35 1 483.34 5 8 6.61 E-4471 36 2 294.5e 6.Se 2-5812 8 1 294.58 6 3 12.91 18688 3 7 667.3e 13.51 21619 3 1 657.38 6 4 13.16 1-1252 2 4 667.38 14.se 2-2863 2 1 667.38 6 5 13.26 1-1454 7 4 667.3s 14.81 2-1545 7 1 657.38 on 6 6 13.29 1-1718 6 3 657.34 14.88 2-9548 6 1 857.38 8 6 7 18.39 1-2286 5 7 483.38 11.10 2-6874 5 1 483.38

[g 6 8 7.24 6-1474 36 2 294.5e 7.43 2-4642 8 1 294.58 7 3 13.68 18824 3 7 667.3e 13.8e 28577 3 1 667.38 7 4 13.81 1-8977 2 4 657.38 14.89 2-2162 2 1 657.18 7 5 14.13 1-1672 1 7 667.38 14.28 2-2477 1 1 667.38 7 6 13.92 1-8257 6 3 667.3e 14.18 2-1774 6 1 667.3e 7 7 12.48 1-4815 5 7 483.38 12.77 2-4187 5 1 483.38 7 8 8.14 1-4175 4 7 294.58 8.59 2-6426 4 1 294.00 8 3 12.16 18888 3 7 667.38 12.84 21844 3 1 667.38 8 4 12.48 1-2789 2 5 667.38 12.38 2-2452 2 1 667.38 8 5 12.74 1-seel 1 7 667.38 12.44 2-2761 1 1 657.38 8 6 12.58 1-2273 6 2 667.3s 12.38 2-2694 6 1 667.38 8 7 11.32 3-4578 5 2 483.38 12.21 2-5786 5 1 483.34 8 8 7.28 1-5417 4 6 294.58 7.43 2-4589 4 1 294. Se 9 3 9.44 18587 3 2 667.38 9.48 31766 3 1 657.38 9 4 9.73 1-8866 2 7 657.3s S.71 3-980s 2 1 667.38 9 5 18.61 1-2828 1 7 667.38 9.85 3-189e 1 1 667.38 9 6 9.78 1-1193 6 2 657.38 9.72 3-2421 6 1 657.38 9 7 8.68 1-8519 5 2 483.38 8.67 3-4146 5 1 483.34 9 8 E.49 1-5239 4 2 294.54 E.69 3-1432 4 1 294.58 t

• 4 b

. , . t . . . .

TABLE 5-19 NAXIWUW FERTILE PARTICLE BURNUP AT 3/32 REStr TS FROW CATT CALCULATIONS ON UNIVAC FSV, CYCLE 3, 294.5 EFPD LAYER SEGMENT FIMA,% BLOCX PATCH COLUhD4 EFPD FIMA,5 BLOCK PATCH COLUh84 EFPD 4 3 .se 1-8065 3 7 657.38 1.85 2-2424 3 1 667.38 4 4 .88 1-1371 2 3 667.38 1.26 2-2998 2 1 667.38 4 5 .85 1-1358 7 5 657.38 1.22 2-9244 7 1 667.38 4 6 .85 1-1989 6 6 667.38 1.21 2-2413 6 1 667.38 4 7 .31 1-4811 5 6 483.38 .48 2-5728 5 1 483.3s 4 8 .14 1-5283 8 2 294.55 .25 2-9059 36 1 294.58 i 5 3 1.54 1-8e43 3 7 667.38 1.77 2-2263 3 1 657.38 5 4 1.67 1-8421 2 2 657.34 2.87 2-2661 2 1 667.3s 6 5 1. '.'s 1-8281 7 6 657.38 2.87 2-2236 7 1 C57.38

, 5 6 1.67 1-1987 6 2 667.38 2.84 2-2739 6 1 657.38 1 5 7 .69 1-8913 5 2 483.38 .91 2-2266 5 1 483.38 1 5 8 .38 1-4155 8 3 294.58 .38 2-5812 8 1 294.58 6 3 1.94 1-8588 3 7 657.38 2.06 2-1519 3 1 65).38 6 4 2.11 1-8289 2 6 657.38 2.36 2-2863 2 1 667.38 6 5 2.14 1-1454 7 4 657.38 2.35 2-1545 7 1 667.38

c. 6 6 2.16 1-1718 6 3 657.38 2.35 2-8548 6 1 667.38 8

6 7 .99 1-2285 6 7 483.38 1.13 2-6874 5 1 483.3e IO 6 8 .39 1-1496 8 3 294.58 44 2-4642 8 1 294.58 7 3 2.87 1-8024 3 7 657.35 2.84 2-8577 3 1 667.36 7 4 2.23 1-9977 2 4 657.38 2.26 2-2162 2 1 667.38

7 5 2.28 1-1392 7 4 667.38 2.27 2-0217 7 1 667.38 l 7 6 2.28 1-8257 6 3 667.38 2.26 2-1774 6 1 667.38

! 7 7 1.27 1-4815 6 7 483.38 1.38 2-4187 5 1 483.3s

7 8 45 1-4175 4 7 294.58 .48 2-5426 4 1 294.58 i

-8 3 1.51 1-8888 3 7 667.38 1.48 2-1944 3 1 667.38 8 4 1.66 1-8694 2 7 667.3d 1.54, 2-2452 2 1 667.38 d 5 1.78 1-8361 7 4 657.38 1.56 2-1226 7 1 667.34 8 8 1.68 1-2273 6 2 657.34 1.54 2-2694 6 1 657.34 8 7 1.Se 1-4578 6 2 483.38 .93 2-5786 5 1 483.38 8 8 .35 1-5417 4 6 294.56 .35 2-4589 4 1 294.54 l 9 3 .75 1-8587 3 2 657.38 .69 3-1766 3 1 667.3e 1 9 4 .83 1-8855 2 7 667.38 .74 3-8888 2 1 667.38 9 5 .85 1-8826 7 3 667.38 .76 3-1755 7 1 667.34 9 6 .r3 1-1193 6 2 667.35 .75 3-2421 6 1 667.38 9 7 .58 1-8519 6 2 483.3d .44 3-4146 5 1 483.34 9 8 .38 1-4849 4 7 234.GS .18 3-1432 4 1 294.54 e

O e

c 0a' 4

b

.- . . 6 . . .

TABLE 5 20 MAX!MJW FERTILE PARTICLE BURNUP AT 3/32 RESULTS FROM DIF3D CALCULATIONS ON CRAY FSV, CYCLE 3, 294.5 EFPD LAYER SEGMENT FIMA,5 BLOCK PATCH COLLaS4 EFPD FIWA,5 BLOCK PATCH COLUhed D*;

4 3 S.82 19865 3 7 667.34 1.88 22424 3 1 657.38 4 4 S.89 1-1371 2 3 657.38 1.29 2-2098 2 1 (57.38 4 5 S.87 1-1368 7 E 657.38 1.24 2-8244 7 1 667.38 4 6 S.86 1-8144 6 2 667.38 1.24 2-2413 6 1 667.38 4 7 S.33 1-4217 5 4 483.38 S.51 2-5728 5 1 483.36 4 8 S.14 1-6283 8 2 294.58 S.28 2-4887 8 1 294.58 5 1 1.56 18843 3 7 667.34 1.01 22263 3 1 667.38 5 4 1.78 1-9555 2 6 657.30 2.11 2-2661 2 1 667.38 5 5 1.72 1-8281 7 5 657.38 2.18 t-2236 7 1 657.3e 5 6 4.78 1-1967 6 2 657.36 2.88 2-2739 e 1 857.33

, 6 7 8.72 1-5913 5 2 483.38 8.95 2-2266 5 1 483.34 j E 8 S.38 1-4155 8 3 294.58 S.39 2-5812 8 1 294.E&

6 3 1.97 ISESS 3 7 667.38 2.18 21519 3 1 667.38 6 4 2.14 1-8289 2 6 657.38 2.39 2-2863 2 1 667.38 g, 6 5 2.17 1-1454 7 4 667.38 2.38 2-1545 7 1 667.38 s 6 6 2.19 1-1718 6 3 667.38 2.39 2-9548 6 1 6E7.38 La 6 7 1-2285 5 7 483.38

1. 1. 1.82 1.17 2-6874 5 1 483.3e  !

6 8 S.38 1-1496 8 3 294.55 S.45 2-4642 8 1 2S4.58 7 3 2.89 19824 3 7 657.38 2.98 28677 3 1 667.30 7 4 2.25 1-9977 2 4 667.38 2.29 2-2162 2 1 857.3e 7 5 2.eG 1-1392 7 4 657.38 2.38 2-8217 7 1 857.38

7 6 2.31 1-8257 6 3 667.38 2.38 2-1774 6 1 657.38 7 7 1.38 1-4815 E 7 483.38 1.34 2-4187 E 1 483.38 7 8 S.47 1-4175 4 7 294.58 S.61 2-5426 4 1 294.58 8 3 1.53 19888 3 7 667.38 1.42 21644 3 1 667.34 8 4 1.67 1-9894 2 7 657.34 1.56 2-2452 2 1 667.36 8 5 1.72 1-8361 7 4 667.35 1.57 2-1226 7 1 667.38 8 6 1.78 1-2273 6 2 657.38 1.56 2-2694 6 1 667.3e 8 7 1.82 1-4578 5 2 483.38 S.95 2-5786 5 1 483.34 8 8 S.36 1-5417 4 6 294.54 S.36 2-4589 4 1 294.58 9 3 S.76 19587 3 2 667.38 S.78 31766 3 1 6E7.34 9 4 8.83 1-9055 2 7 657.38 S.75 3-8888 2 1 667.38 9 5 S.85 1-8826 7 3 657.38 S.77 3-1766 7 1 657.38 9 6 S.84 1-1193 6 2 667.38 S.70 3-2421 6 1 657.38 9 7 S.51 1-8519 5 2 483.34 8.46 3-4146 5 1 483.38 9 8 S.18 i-4849 4 7 294.58 8.18 3-1432 4 1 294.54 e

O e

k La 0%

o

• * ** ~ *

.- , . s .. ..

TABLE 5-21 RADIAL BURNUP DISTRIBUTION NEAR CORE MIDPLANE Gr888 Per Element. Element MWD, Region,f*f .wJ Z Difference in Burnup Column. Core and Location Layer Element 3-D Code EFPD Th-232 U-233 U-235 U-236 U-238 I Difference Midplane, 1, 4, 7 1-1237 CATT 170.4 10,653.3 200.9 90.28 45.58 19.54 365.53 Ring 1 GATT 294.5 10.570.9 215.7 69.27 48.37 19.02 440.59 DIF3D 294.5 10,567.0 21. ? 68.37 48.49 19.00 444.17 5Z s2 4Z 42 41 4.8%

Ring 2 7, 6, 7 1-0133 GATT 170.4 8,863.3 179.2 119.1 62.60 26.00 432.49 GATT 294.5 8,802.6 137.1 93.6 55.88 25.41 498.66 DIF3D 294.5 8,800.1 187.2 92.6 66.01 25.39 501.47 4Z 1Z 4Z 4Z 3Z 4.2Z Y Ring 3 18, 6, 7 15217 CATT 170.4 9,851.7 172.0 152.7 48.55 23.89 309.44 U GATT 294.5 9,784.8 188.5 120.0 53.42 23.33 378.35 DIF3D 294.5 9,784.4 188.3 119.6 53.48 23.33 379.20 12 -1Z 1Z 12 01 1.22 Ring 4 25. 1, 7 2-5848 CATT 170.4 4.940.9 32.31 294.1 15.62 22.67 62.69 GATT 294.5 4,908.1 54.40 236.1 26.03 22.14 116.36 DIF3D 294.5 4,908.4 54.27 237.1 25.87 22.14 115.34

-1Z -12 -2Z 2Z OZ -1.9Z Buffer 35, 6, 7 5-6056 GATT 170.4 10,484.9 112.2 329.8 51.12 36.51 255.23 Element GATT 294.5 10,425.9 135.9 256.9 62.98 35.88 342.23 DIF3D 294.5 10.430.7 134.9 264.1 61.82 35.93 333.27

-8Z -4Z -10Z -10Z -8Z -10.3Z (a)See Fig. 5-3 for locations of columns.

(b)This axial layer is just below the core midplane. $

k n

4 l

i TABLE 5-22 ~1 AXIAL BURNUP DISTRIBUTION NEAR CORE CENTERLINE Grams per Element,

'E' "* and Z Difference in Burnup Element MWD Column. Core and Location Layer Element 3-D Code EFPD Th-232 U-233 U-235 U-236 U-238 I Difference i

Core Top 1, 4, 4 1-0708 GATT 170.4 13,171.8 148.3 253.7 35.98 26.41 193.51 j GATT 294.5 13,132.2 227.8 40.35 168.4 26.10 230.31

] DIF3D 294.5 13,127.3 170.7 224.6 40.88 26.06 234.97 12Z 11Z 12Z 12Z 13Z 12.72 1

, 1, 4, 5 1-1770 GATT 170.4 12.540.3 199.8 193.6 46.96 25.59 289.96 I GATT 294.5 12.479.4 221.9 165.5 51.40 25.08 345.14

) DIF3D 294.5 12,473.5 223.6 162.7 51.81 25.04 350.79 10Z 8Z 10Z 92 8Z 10.2Z 9 [ 1, 4, 6 1-1445 GATT 170.4 12.197.3 327.1 136.8 54.41 24.47 393.15 s-

! GATT 294.5 12.114.9 248.1 110.2 58.14 23.84 468.35

DIF3D 294.5 12,109.5 249.1 108.5 58.37 23.80 473.52 j 7Z 6Z

-1Z 6Z 6Z 6.9Z 1, 4, 7 10.653.3 d

1-1237 GATT 170.4 200.9 90.28 45.58 19.54 365.53 GATT 294.5 10,570.9 215.7 69.27 48.37 19.02 440.59 DIF3D 294.5 10.567.0 216.2 68.37 48.49 19.00 444.17 5Z 3Z 4Z 4Z 4Z 4.8%

1, 4, 8 1-1360 GATT 170.4 10.797.9 182.4 115.3 41.94 20.03 299.82 GATT 294.5 10,723.7 200.6 89.9 45.65 19.57 367.87 DIF3D 294.5 10.720.6 201.3 89.0 45.79 19.55 370.65 4Z 4Z 4Z 4Z 4Z 4.1Z e

Core 1, 4, 9 1-2489 GATT 170.4 11,906.7 146.5 147.9 29.99 18.61 188.17 3 Bottom GATT 294.5 11,851.0 168.5 122.3 34.13 18.32 236.98 b DIF3D 294.5 11,848.7 169.5 121.5 34.26 18.31 238.74

! 42 4Z 37 3Z 3Z 3.5Z fp i

j

..~ _ . - . ..

i e i l

909436 N/C j' TABLE 5-23 i AXIAL BURNUP IN REGION 1, COLUMN 4 "

DURING CYCLE 3 FROM 170.4 TO 294.5 EFPD Axial Average APF Element GATT DIF DIF/GATT GATT DIF DIF/GATT 4 36.80 41.46 1.127(*) 0.615 0.650 1.057 5 55.18 60.83 1.102 0.922 0.954 1.035 l 6 75.20 80.37 1.069 1.256 1.260 1.003 i 7 75.06 78.64 1.043 1.254 1.233 0.983 8 68.05 70.83 1.041 1.137 1.110 0.976 9 48.81 50.57 1.036 0.816 0.793 0.972 Total 359.1 382.7 1.066(b) 1,000 1,ono *

~

(*)1.127 = 1.066 (radial factor) x 1.057 (axial factor).

(b) Agrees with average RPF for patch 1, column 4.

i i  :

q ,

l t

) I i

a I j  !

l h

,. 5-55 I t

i

909436 N/C Tables 5-17 and 5-18 give the fissile particle burnup at time point 3/32 calculated by the GATT and nodal DIF3D codes. Standard column data is separated from control column data. Tables 5-19 and 5-20 give the

, results for the fertile particle burnup. In general, the particle burn-ups are in fairly good agreement. The largest difference was 5.1% in the fissile particle burnup for Segment 8 in the top layer of the core.

He ever, comparing particle burnups in Tables 5-17 to 5-20 can be deceptive, because the particle burnups are for their entire core residence time and are not just for the 170.4 to 294.5 EFPD period of Cycle 3 during which different fluxes were calculated with the GATT and nodal DIF3D codes.

Tables 5-21 and 5-22 were developed to compare the incremental burnup during the 170.4 to 294.5 EFPD period of Cycle 3. Table 5-21

- gives the burnup in five fuel elements located in the layer just below the core midplane. The percent difference in the nuclide burnups agree well with the percent difference in the element megawatt days (MWD), as they should. The percent difference in the element MWD results from the different radial power distributions calculated by GATT versus the nodal DIF3D (shown in Appendices B-2 to B-14). The 10.3% lower burnup for buffer element 5-6056 indicates again that the nodal DIF3D code calcu-lates a lower part at the core-radial reflector interface than the GATT code.

Table 5-22 gives the burnup for each of the six elements along the axial height of a standard column in the central region of the core.

The difference in the element MWD between the GATT and the DIF3D cal-culations varies from 3.6% to 12.7%. This difference is caused by an average DIF3D/GATT RPF ratio of 1.066 between 170.4 and 294.5 EFPD of Cycle 3. This value is shown in Table 5-23. Also contributing to the 12.7% difference in the calculated MWD for the top element is a differ-

. ence in the calculated axial peaking factor of about 3%, arrived at by comparing the region 1, block i value in Table 5-9 from GATT with the 5-56 i

n- , -

1.

909436 N/C l

l l region 1, level 1 value in Table 5-10 from DIF3D. For the top two ele-ments in region 1, column 4, there is an additional effect due to the presence of the control rod in the top two core layers of region 1

. throughout the 170.4 to 294.5 EFPD period in both the GATT and DIF3D calculations (Table 5-11). This difference in the calculated standard column / control column power split for a rodded layer evidently adds another 2% difference to the GATT versus DIF3D MWD burnup for the top element of region 1, column 4.

Calculated 45"+'orences between GATT and DIF3D of these three power distributions ( edia', . axial, and standard / control column) combined to cause the largess difference in the calculated element MWD, which occurs in the top element of a standard column in region 1 (the 12.7% d!'fer-ence in Table 5-22). The opposite extreme would occur in the top layer of the core in an element next to the rad v. ceflector. Mcwever, in 4

, spite of these relatively large difference.' these locations, burnups calculated with GATT and DIF3D for most fusi elements should fall within b about 5% of each other. This is acceptable similarity for establishing the validity of the DIF3D code.

1 l 4 6

5-57

909436 N/C 1

1 1

1

6. 3D BURNUP FOR CYCLE 4 Using the same three-dimensional model (Fig. 5-4) that was used for j the Fort St. Vrain Cycle 3 calculations discussed in Section 5, nodal l DIF3D calculations were also done for the 4.9 to 24.9 EFPD period in 1

Cycle 4. The calculational sequence was similar to that given in Fig. 5-1. The power history used over this period of Cycle 4 is given l in Table 6-1, and the control rod withdrawal sequence for Cycle 4 is given in Table 6-2. These DIF3D calenlations for Cycle 4 cover the same time period as previous GATT calculations.

l ,

Appendix C shows the GATT/DIF3D radial power distribution l

~

comparisons for the 4.9 to 24.9 EFPD period of Cycle 4. The 6rca is I

summarized in Table 6-3. Comparing this table with Tables 5-6 and 5-8 t . .

for the Cycle 3 calculations indicates general similarities:

1. The Ak between GATT and DIF3D was relatively small, about l

' O.001 to 0.002, i.e., similar to the reactivity discrepancy observed in Cycle 3.

2. DIF3D cc)culated about 6% lower powers in the outer regions of l the core next to the reflector. This was also observed in Cycle 3 burnup calculations.

l I

l l 3. The one sigma standard deviation of the percent difference l

between the GATT and DIF3D RPFs is about 7% at the start of f* the burnup period.

~

Appendices B and C indicate that both sets of calculations have the largest RPF differsnee in the northwest sector of the core where the region km is the highest.

i l

l 6-1

909436 N/C TABLE 6-1

, POWER HISTORY USED FOR 3-D CALCULATIONS IN CYCLE 4 WITH GATT AND DIF3D Time Point for 3-D Core Burnup Calendar Core Shim Bank Internal (EFPD) Days Power, MW Position (a) Beginning End 4.9 to 8.9 43.48 75.8 4E full out 4 5 8.9 to 17.4 24.72 290.0 3C at 2/6 6 7 17.4 to 24.9 25.12 253.0 30 at 2/6 8 9 (a) Fraction Inserted. Regulating rod position in region 1 was kept at a constant-insertion position of two out of six fuel layers; i.e.,

2 x 31.22 in. = 62.44 in. Inserted, or 4 x 31.22 in. = 124.88 in, withdrawn.

TABLE 6-2 FSV CONTROL ROD WITHDRAWAL SEQUENCE FOR CYCLE 4 Withdrawal Sequence Group Regions 1 2A 2,4,6 2 4F 25, 31, 37 3 4D 23, 29, 35 3A 1 (half out) 1 4 4B 21, 27, 33 5 2B 3,5,7 6 4E 24, 30, 36 7 4A 20, 26, 32 8 4C 22, 28, 34

, 9 3C 10, 14, 18 10 3A 8, 12, 16 11 3B 9, 13, 17 12 3D 11, 15, 19

, 13 1 (last half) 1 6-2

909436 N/C

^

. TABLE 6-3

SUMMARY

OF GATT/DIF3D COMPARISON FOR CYCLE 4 l

Cycle / k-eff Average % One Sigma Time Difference for for Appendix Point EFPD GATT D1F3D Ak Regions 20-37. Regions 1-37 C-2 4/4 4.9 1.0165 1.0199 0.0034 -6.10 8.64 C-3 4/5 8.9 1.0039 1.0069 0.0030 -4.47 5.94 C-4 4/5 8.9 1.0212 1.0202 -0.0010 -5.76 7.54

! C-5 4/6 17.4 1.0050 1.0044 -0.0006 -5.90 7.72 l C-6 4/7 17.4 1.0061 1.0056 -0.0005 -5.89 7.66 C-7 4/8 24.9 1.0055 1.0049 -0.0006 -5.32 6.77 ee l

1 m

O e

e 6-3

909436 N/C This RPF difference is the largest at the beginning of the burnup period

, , and decreases as xenon builds up and fissile material burnup occurs.

. These similarities indicate that the Cycle 4 DIF3D calculations are essentially consistent with the Cycle 4 GATT calculations and with the Cycle 3 GATT/DIF3D comparisons. This justifies the use of the DIF3D code for the FSV burnup calculations starting from 25 EFPD of Cycle 4.

• e 6

5 e

6 e

6-4

l z

909436 N/C

, 7. DOCUMENTATION CONTROL 7.1. CODE VERSIONS Section 5.2 and Fig. 5-1 summarize the calculational segur.nces thac were used for the 2-D and 3-D DIF3D calculations involved in this study.

The codes that were used are as follows:

UNIVAC UNIVAC Controlled Program Code Version Library No.

GAUGE MOD 25 RPSD 3760 BUGTRI REF RPSD 4069 FSVCOR /DC87 SYSD 5013 POKEGT S GATMAC l CRAY symbolic of these codes is

., GZINT 4

archived via the UNIVAC archive BUGATT j system as RPSD 2775 on a VAX GEOMETRY tape.

DIF3D-5.3/6 DIFPOW (APF) l FUELED /

7.2. DATA STORAGE The SDSU CRAY system files related to the 3-D DIF3D calculations for FSV Cycle 3 discussed in Section 5 have been microfiched as follows:

Time Related Input Microfiche Output Microfi.he Pc3 .nt Code File Sheets File Sheets 3/20 GATMAC gatmac20 1 out1 1 POKE poke 20 1 out2 1 favcordt 1

', GZINT gzint20 1 out3 1 dens 20 1

, GEOMETRY geomC3 1 out4a 1 cards 30 1 BUGATT bugatt20 1 out5 1 DIF3D dif20 2 out6 2 7-1

909436 N/C Time Related Input Microfiche OutputMicrofiche Point Code File Sheets File Sheets

',' DIFPOW difpow20 1 out7 1 russdata 1 3/21 BUGATT bugatt21 1 out8 1 DIF3D dif21 2 out9 2 DIFPOW difpow21 1 out10 1 3/22 GATMAC gatmac22 1 outil 1 POKE poke 22 1 out12 1 GZINT gzint22 1 out13 1 BUGATT bugatt22 1 out15 1 DIF3D dif22 2 out16 2 DIFPOW difpow22 1 out17 1 3/23 BUGATT bugatt23 1 out18 1 DIF3D dif23 2 out19 2 DIFPOW difpow23 1 out20 1 3/24 GATHAC gatmac24 1 out21 1 POKE poke 24 1 out22 1 GZINT gzint24 1 out23 1 BUGATT bugatt24 1 out25 1 DIF3D dif24 2 out26 2

. DIFPOW difpow24 1 out27 1 3/25 BUGATT bugatt25 1 out28 1 DIF3D dif25 2 out29 2

~

DIFPOW difpow25 1 out30 1 3/26 GATMAC gatmac26 1 out31 1 POKE poke 26 1 out32 1 GZINT gzint26 1 out33 1 BUGATT bugatt26 1 out34 1 DIF3D dif26 2 out35 2 DIFPOW difpow26 1 out36 1 3/27 BUGATT bugatt27 1 out37 1 DIF3D dif27 2 out38 2 DIFPOW difpow27 1 out39 1 3'28 BUGATT bugatt28 1 out44a 1 DIF3D dif28 2 out45 2 DIFPOW difpov28 1 out46 1 3/29 BUGATT bugatt29 1 out47 1 DIF3D dif29 2 out48 2 DIFP0W difpow29 1 out49 1 3/30 BUGATT bugatt30 1 outs 0 1 DIF3D dif30 2 outs 1 2 DIFP0W difpow30 1 outs 2 1 3/31 GATHAC gatmac31 1 outs 3 1 POKE poke 31 1 outs 4 1 l -

~

GZINT gzint31 1 outSS 1 i BUGATT bugatt31 1 outs 6 1 l

~

DIF3D dif31 2 outs 7 2 DIFP0W difpow31 1 outs 8 1 7-2

909436 N/C Time Related Input Microfiche Output Microfiche Point Code File Sheets File Sheets

.- 3/32 BUGATT bugatt32 1 outs 9 1 DIFSD dif32 2 out60 2 DIFPOW difpow32 1 out61 1

, 3/25 FUELED fueled 25 1 out62 8 favassc3 1 out63 2 3/32 FUELED fueled 32 1 out64 8 out65 2 3/25 FIMA fimain 1 out66 1 3/32 FIMA Ifima _1 out67 _1 76 91 The above files, together with several density and microscopic cross section flies, were initially located on SDSU CRAY directory DIFVALC3. Their permanent storage location is archived on tape as VAX entry 909436DIFVAL (RPSD2747) in the GA archive library system.

,, GA UNIVAC files related to 2-D calculations, and editing of 3-D calculations,.have been microfiched as follows:

Description Sheets

1. GAUGE ST8465, TP640, Doubled Ref. Imp. 1

2. GAUGE ST9529, TP640, As-built Ref. Imp. 1

3. BUGTRI ST2124, TP640, As-built Ref. Imp. 2

4. GAUGE ST2346, TP650, Doubled Ref. Imp. 1

5. GAUGE ST2408, TF650, As-Built Ref. Imp. 1

6. BUGTRI ST7684, TP650, As-Built Ref. Imp. 2

7. RPF for TP640 and 650 1

8. FIMA on 3/32 GATT 1

9. RPF for 3-D cales., Cycle 3 1

10. RPF for 3-D cales., Cycle 4 _1

,- 12 4

S 7-3

909436-N/C' On paper output are the following:

. No. of Job No. Description Pages

1. Munoz POKE, TP 650 22

2. ST'6460 FSVCOR, 3/21, 23, and 25 20

3. ST 6461 FSVCOR, 3/27, 29, 30 and 32 20

4. ST 9860 Region Power Calc. for BUGTRI, TP 640 12

5. ST 3799 GATT map for Cycle 3 20 94 64 l-4 4

i9 9

7-4

909436 N/C

. 8. REFERENCES

1. Wagner, M., and K. Koebke, "Progress in Nodal Reactor Analysis,"

ANS Topical Conference on Computational Methods, Salt Lake City, Utah, CONF-830304-16 (March 1983).

2. Dorning, J. J., "Modern Coarse-Mesh Methods: A Development of the 70's," Proc. of ANS Topical Mtg. on Comp. Methods in Nuc. Eng.,

Williamsburg, Virginia (April 1979).

3. Wagner, M. R. , "Current Trends in Multidimensional Reactor Calculations," Conf. on Comp. Methods in Nuc. Eng., Charleston Souch Carolina, CONF-750413 (April 1975).

4. Adams, C. H., "Current Trends in Methods for Neutron Diffusion

, Calculations," Nuc. Sci, and Eng., 64, 552 (1977).

5. Lathrop, K. D., "Computational Procedures for Multidimensional Core Analysis," ANS Topical Conf. on Advances in Reactor Physics, Gatlinburg, Tennessee (April 1978).

6. Frohlich, R., "Summary Discussion and State-of-the-Art Review for Coarse-Mesh Computational Methods," Atomkernenerale, 30, 152 (1977).

7. White, J. R., "Overview of Hexagonal Nodal Methods for HTGR Applications," GA Technologies Document 909614, January 1988.

8. Lawrence, R. D., "The DIF3D Nodal Neutronics Option for Two- and Three-Dimensional Diffusion Theory Calculations in Hexagonal Geometry," ANL-83-1, Argonne National Laboratory (March 1983).

9. Delp, D. L., et al., "FLARE: A Three-Dimensional Boiling Water Reactor Simulator," GEAP-4598, General Electric Company (1964).

. 10. Goldstein, L., F. Nakache, and A. Veras, "Calculation of Fuel-Cycle Burnup and Power Distribution of Dresden-I Reactor With the TRILUX Fuel Management Program," Trans. Am. Nuc. Soc., 10, 300 (1967).

8-1

909436 N/C

11. Borresen, S., "A Simplified, Coarse-Mesh, Three-Dimensional

,, Diffusion Scheme for Calculating the Gross Power Distribution in a Boiling Water Reactor," Nuc. Sci. and Eng., 44, 37 (1971).

. 12. Robinson, C. P., and J. D., Eckard, Jr., "A Higher-Order Difference Method for Diffusion Theory," Trans. Am. Nuc. Soc., 15, 297 (1972).

13. VerPlanck, D. M., et al., "SIMULATE-Et A Nodal Core Analysis Program for Light-Water Reactors," NP-2792-CCM, Electric Power Research Institute (March 1983).

14. Finneman, H., F. Bennewitz, and M. R. Wagner, "Interface Current Techniques for Multidimensional Reactor Calculations," Atomkern-eneraie, 30, 123 (1977).

15. Bennewitz, F., H. Finnemann, and H. Holdaschl, "Solution of the Multidimensional Neutron Diffusion Equation by Nodal Expersion,"

Conf. on Comp. Methoda in Nuc. Eng., Charleston, South Gaeolina, CONF-750413 (April-1975).

~ 16. Maeder, C., "A Nodal Diffusion Method With Legendre Polynomials,"

ANS Topical Conf. on Advances in Reactor Physics, Gatlinburg, Tennessee (April 1978).

17. Greenman, G., K. Smith, and A. F. Henry, "Recent Advances in an Analytic Nodal Method for Static and Transient Reactor Analysis,"

Proc. of the ANS Topical Meeting on Computational Methods in Nuc.

Eng., Williamsburg, Virginia (April 1979).

18. Shober, R. A., "A Nodal Method for Fast Reactor Analysis," Proc. of the ANS Topical Meg. on Comp. Methods in Nuc. Eng., Williamsburg, Virginia (April 1982).

19. Duracz, T., "A Nodal Method in Hexagonal Geometry," ANS Topical Meg. in Adv. in Math Methods for the Soln. of Nuc. Eng. Problems, Munich, Germany (April 1981).

20. Lawrence, R. D., "A Nodal Method for Three-Dimensional Fast Reactor Calculations in Hexagonal Geometry," ANS Topical fonf. on Computational Methods, Salt Lake City, Utah, CONF-830304-16 (March 1983).

. 21. Derstine, K. L., "DIF3D: A Code to Solve One , Two , and Three-Dimensional Finite Difference Diffusion Theory Problems,"

ANL-82-64, Argonne National Laboratory (April 1934).

8-2

909436 N/C f 22. Wagner, M. R., "GAUGE: A Two-Dimensional Few-Group Neutron

,, Depletion Program for a Uniform Triangular Mesh," USAEC Report t

GA-8547 (1968). {

.. 23. Kraetsch, H., and M. R. Wagner, "GATT: A Three-Dimensional Few-Group Neutron Diffusion Theory Program for a Hexagonal-Z Mesh,"

l USAEC Report GA-8547, Gulf General Atomic (January 1969). ,

i L 24. Vondy, D. R., and T. B. Fowler, "Neutronics Code Validation for Two-Dimensional Triagonal (Hexagonal) and Three-Dimensional Geometries," ORNL-5792, Oak Ridge National Laboratory (1981).

25. Archibald, R. J., and P. K. Koch, "A User's and Programmer's Guide to the GAUGE Two-Dimensional Neutron Diffusion Program," GA-A16657 (1983).

26. Little, W. W. Jr., and R. W. Hardie, "2DB User's Manual -- Rev. 1,"

BNWL-831 Rev. 1 (1969).

, 27. Lawrence, R. D., and J. J. Dorning, "A Nodal Green's Function Method for Multidimensional Neutron Diffusion Calculations," Nuc.

S_ci. Engr., 76, 218 (1980).

28. Davison, W. R., "BUG 180/HTGR: A Two-Dimensional, Triangular Mesh, Multigroup Diffusion-Burnup Code for Use in the Design of 180-Deg Rotationally Symmetric HTGR Cores," GA-A12674 (1975).

29. Dorsey, J. P., R. Froehlich, and F. Todt, "BUG-2/BUGTRI, Two-Dimensional Multigroup Burnup Codes for Rectangular and Hexagonal Geometry," GA-8272 (1969).

30. Toppel, B. J., et al., "Validation of Alternative Methods and Data for a Benchmark Fast Reactor Depletion Calculation," ANS Topical Meg. on Adv. In Reactor Physics and Core Thermal Hydraulics, Kiamesha Lake, New York (1982).

31. Pfeiffer, W., G. Malek, and K. Lund, "POKE: A Gas-Cooled Reactor j Flow and Thermal Analysis Code," GA-10226, July 16, 1970,

, SYSD 3623.

8-3

909436 N/C

. APPENDIX A TWO-DIMENSIONAL RADIAL PEAKING FACTOR COMPARISONS AT TIME POINTS 640 AND 650 e

6 l

t l

l A-1 I

l l

l 1 .

2-D calculations RPF COMPARISDN FOR TIME P3 INT C43 0F FSV, CYCLE 3

2. PSC GAUGE, TP645, 7-CROUPS, AS-BUILT REFLECTOR IMP. Km 1. ele 2 IS COMPARED TO THE REFERENCE CALCULATION :

1. CA BUCTRI, TP648, 7-CROUPS, AS-BUILT REF. IMP., E-5 CONV. Km 1.8096

1. CA BUCTRI, TP646, 2. PSC CAUCE, TP648, REC 35 REC 36 REC 37 REC 2e REC 35 REC 36 REC 37 REG 2e

.89 1.58 1.15 .79 1.81 1.82 1.31 .89 REC 34 REC 18 REG 19 REG 8 REC 21 REC 34 REGIS REC 19 REG 8 REC 21

.78 .68 .84 .83 .59 .83 .78 .87 .86 .63 REG 33 REC 17 REG 7 REG 2 REG 9 REC 22 REG 33 REG 17 REG 7 REG 2 REG 9 REG 22

.53 .80 .98 .86 .63 .68 .52 .76 .93 .83 .68 .68 REC 32 REGI6 REG 6 REG 1 REG 3 RECis REC 23 REC 32 REC 16 REG 6 REG 1 REC 3 REGls REG 23 1.24 .75 1.85 1.11 1.16 .86 .55 1.75 .78 .96 1.84 1.84 .84 .57 REG 31 REGIS REG S REG 4 REC 11 REC 24 REC 31 REC 15 REG 5 REG 4 REC 11 REC 24 1.18 1.25 1.74 1.74 1.11 1.34 1.15 1.14 1.59 1.63 1.15 1.44 REC 3e REC 14 REC 13 REC 12 REC 25 REG 3e REC 14 REC 13 REC 12 REG 25 1.04 .84 .83 .94 2.11 .99 .76 .76 .93 2.31 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26

.55 1.07 .68 1.16 .51 1.e4 .38 1.27 bJ Km 1.0096 K= 1.6182 REGIONS AVC. % DIF. ONE SIGMA  % DIFFERENCE i

1 - 19 -4.20 4.15 REC 35 REC 36 REC 37 REG 2e 13 16 14 13 28 - 37 4.34 7.81 REC 34 REC 18 REC 19 REG 8 REC 21

, 1 - 37 .04 7.11 5 3 3 3 5 REC 33 REC 17 REG 7 REC 2 REG 9 REC 22

-1 -5 -4 -4 -4 1 REC 32 REGlo REG 8 REC 1 REG 3 REcle REC 23 1 -7 -8 -7 -5 -2 3 REG 31 REC 15 REG S REC 4 REC 11 REG 24

-3 -9 -9 -6 -1 7 REC 3e REG 14 REC 13 REC 12 REC 25

-5 -le -8 -1 le v3 C)

REC 29

-6 REC 28

-4 REC 27 REC 26 j)

0 9 o.

m DELTA Km .0006 2:

i O

2-D calculctions RPF COMPARISON FOR TIME POINT C43 DF FSV, CYCLE 3

3. PSC NODAL DIF3D TP 648, 7-GROUPS, AS-BUILT REF, IWP. Km 1.0890 IS COMPARED TO THE REFERENCE CALCULATION :

1. CA BUCTRI, TP648, 7-CROUPS, AS-BUILT REF. IMP., E-5 CONV. K= 1.0096

1. CA BUCTRI, TP648, 3. PSC NODAL DIF3D REC 35 REC 36 REC 37 REC 2e REC 35 REG 36 REC 37 REC 2e

.89 1.58 1.15 .79 .83 1.45 1.08 .7G REC 34 REC 18 REC 19 REG 8 9EC21 REC 34 REC 18 REC 19 REG S REC 21

.78 .68 .84 .83 .59 .76 .78 .86 .84 .58 l REC 33 REC 17 REC 7 REG 2 REG 9 REC 22 REC 33 REC 17 REG 7 REG 2 REG 9 REG 22

.53 .88 .98 .86 .63 .6e .51 .83 1.83 .91 .67 .66 REG 32 REC 16 REG 6 REG 1 REG 3 REC 18 REC 23 REG 32 REGIS REC 6 REG 1 REC 3 RECle REC 23 1.24 .75 1.05 1.11 1.18 .86 .55 1.11 .77 1.11 1.18 1.17 .89 .53 REC 31 REC 15 REG 5 REG 4 REC 11 REC 24 REC 31 REGIS REG S REC 4 REC 11 REC 24 1.18 1.25 1.74 1.74 1.11 1.34 1.12 1.28 1.85 1.82 1.14 1.26 REC 3e REG 14 REC 13 REC 12 REC 25 REC 35 REC 14 REGI3 REG 12 REG 25 1.e4 .84 .83 94 2.11 1.02 .89 .88 .96 1.92 REC 29 REC 28 REC 27 REC 26 REG 29 REC 28 REC 27 REC 26

.55 1.07 .68 1.16 .54 1.06 .67 1.07

$3 Km 1.0096 Km 1.0096 REGIONS AVC. X DIF. DNE SICWA 2 DIFFERENCE 1 - 19 4.47 1.88 REC 35 REC 36 REC 37 REC 2e

. -8 -8 -6 -5 20 - 37 -4.55 3.67 REC 34 REC 18 REC 19 REG 8 REC 21 1 - 37 .08 5.21 -3 2 2 2 -2 REC 33 REC 17 REG 7 REC 2 REC 9 REC 22 i -3 4 6 6 6 1 REC 32 REC 16 REG 6 REC 1 REC 3 REC 18 REC 23 l -le 3 7 6 6 3 -3 REC 31 REGIS REG 5 REG 4 REC 11 REC 24

-5 3 6 6 3 -6 REC 3e REC 14 REC 13 REG 12 REC 25 y)

-2 6 7 2 -9 w>

4 I REC 29 REC 28 REC 27 REC 26 $l

-1 -2 -2 -8 Z

DELTA Km .0006 N

2-D calculations RPF COMPARISDN FOR TIME POINT SCO DF FSV, CYCLE 3

4. PSC 6-TRI/ HEX DIF TP648, 7-CR00PS, AS-BUILT REF. IMP. Km 1.8113 IS COMPARED TO THE REFERENCE CALCULATION :

1. CA BUCTRI, TP640, 7-CROUPS, AS-BUILT REF. IMP., E-5 CONV. Km 1.0096

1. CA BUGTRI, TP648, 4. PSC 6-TRI/ HEX DIF l

j REC 35 REC 36 REC 37 REC 2e REC 35 REC 36 REC 37 RE028

.89 1,58 1.15 .79 .82 1.44 1.87 .14 REC 34 REC 18 REC 19 REC 8 REC 21 REC 34 REGIS REC 19 REG 8 REC 21

.78 .68 .84 .83 .59 .76 .78 .87 .85 .59 REG 33 REC 17 REG 7 REC 2 REG 9 REC 22 REC 33 REC 17 REG 7 REC 2 REC 9 REC 22

.53 .86 .98 .86 .63 .68 .52 .84 1.83 .91 .68 .61 l REC 32 REC 16 REC 6 REG 1 REC 3 REcle REC 23 REC 32 REC 16 REG 6 REG 1 REG 3 REC 18 REC 23 1.24 .75 1.06 1.11 1.18 .86 .55 1.18 .78 1.11 1.17 1.16 .98 .54 REC 31 REC 15 REG 5 REG 4 REC 11 REC 24 REC 31 REC 15 REG S REG 4 REC 11 REC 24 1.18 1.25 1.74 1.74 1.11 1.34 1.11 1.29 1.85 1.81 1.14 1.25 REC 3s REC 1, REGIS REC 12 REC 25 REC 3e REC 14 REGIS REC 12 REC 26 1.e4 .84 .83 .94 2.11 1.82 .98 .90 .97 1.89 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26 l .55 1.07 .68 1.16 .55 1.87 .67 1.05 b Km 1.0096 i Km 1.0113 j REGIONS AVC. 5 DIF. ONE SIch X DIFFERENCE i'

1 - 19 4.95 1.75 REC 35 REC 36 REC 37 REC 2s

-8 -9 -7 -6 28 - 37 -4.66 3.98 REC 34 REC 18 HEG19 REG 8 REC 21 1 - 37 .27 5.69 -3 4 3 3 -1 REC 33 REC 17 REC 7 REC 2 REG 9 REC 22

-2 5 5 6 8 1 REC 32 REGIS REC 6 REC 1 REG 3 REC 18 REC 23

-11 4 6 5 6 4 -2 REC 31 RFGIS REG S REG 4 REC 11 REC 24 i,

-6 . 6 4 3 -7 REC 38 REC 14 REC 13 REC 12 REC 25

-2 6 8 3 -le e

REG 29 REC 28 REC 27 REC 26 Cj 8 -1 -1 -le e u

DELTA Km .0017

• l 1

z O

I 1

2-D calculations RPF COMPARISON FOR TIME POINT C49 0F FSV, CYCLE 3

5. PSC 24-TRJ/ HEX DIF, TP648, 7-CROUPS, AS-BUILT REF. IMP. Km 1.818e IS COMPARED TO THE REFERENCE CALCULATXON :

1. GA BUGTRI, TP648, 7-GR0 BPS, AS-BUILT REF. IMP., E-5 CONV. K= 1.0096

1. GA BUCTRI, TP648, 5. PSC 24-TRI/ HEX DIF I

REC 35 REC 36 REC 37 REC 2e REC 35 REC 36 REC 37 REC 2e l

.89 1.58 1.15 .79 .86 1.52 1.12 .77 l REC 34 REC 18 REC 19 REG 8 REC 21 REC 34 REG 18 REC 19 REG 8 REG 21

.78 .68 .84 .83 .59 .77 .78 .87 .85 .68 REC 33 REC 17 REG 7 CEG 2 REG 9 REC 22 REG 33 REG 17 REG 7 REG 2 REG 9 REG 22

.53 .88 .98 .86 .63 .68 .52 .82 1.81 .89 .66 .68 REC 32 REGlo REG 6 REG 1 REG 3 hECIS REC 23 REG 32 REGI6 REG 6 REG 1 REG 3 RECIS REC 23 1.24 .75 1.95 1.11 1.10 .86 .55 1.14 .76 1.08 1.15 1.14 .88 .54 REC 31 REGIS REG 5 REG 4 REC 11 REC 24 REG 31 REGIS REG S REG 4 REG 11 REG 24 1.18 1.25 1.74 1.74 1.11 1.34 1.13 1.26 1.88 1.78 1.13 1.29 REC 38 REG'.4 REC 13 REC 12 REC 25 REC 3e REG 14 REGIS REG 12 REC 25 1.e4 .84 .83 .94 2.11 1.92 .87 .86 .95 1.98 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REG 27 REC 26

.55 1.97 .68 1.16 .54 1.06 .67 1.16 Y K= 1.0896 K= 1.elee u

REGIONS AVC. 5 DIF. ONE SICMA N DIFFERENCE 1 - 19 2.83 1.93 REC 35 REC 36 REC 37 REC 2e

-3 -3 -2 -2 29 - 37 -2.62 2.28 REC 34 REGIS REG 19 REG S REG 21 1 - 37 .18 3.26 -1 3 3 2 1 REC 33 REC 17 REC 7 REG 2 REG 9 REC 22

-2 3 4 4 5 1 REC 32 REC 16 REG 6 REG 1 REG 3 REGle REC 23

-8 1 3 3 4 2 -1 REC 31 REGIS REG 5 REG 4 REC 11 REC 24

-4 1 3 2 2 -4 REC 3e REC 14 REC 13 REC 12 REC 25 u)

-3 3 4 1 -6 $$

n REG 29 REC 28 REC 27 REC 26 'a

-1 -1 -1 -6 2:

DELTA Km .0004 3

4 2-D calculations.

RPF COMPARISDN FOR TIME POINT G4e OF FSV, CYCLE 3 i

3. PSC NOOAL DIF3D TP 848 7-GROUPS AS-BUILT REF. IMP. Km 1.009e IS COMPARED TO THE REFERdNCE CALCUL1 TION

2. PSC GAUGE, TP648, 7-GROUPS, AS-BUILT REFLECTOR IMP. Km 1. ele 2

2. PSC GAUGE, TP648, 3. PSC NODAL DIF3D REC 35 REC 36 REC 37 REC 2s REG 36 REG 36 REC 37 REG 2e 1.01 1.82 1.31 .89 .83 1.45 1.58 .75 REC 34 REGIS REGI9 REG S REC 21 REC 34 REGIS REG 19 REG S REC 21

.83 .78 .87 .86 .63 .76 .78 .86 .84 .58

REC 33 REG 17 REG 7 REG 2 REG 9 REG 22 REC 33 REG 17 REG 7 REG 2 REG 9 REC 22

.52 .76 .93 .83 .Se .Se .51 .83 1.83 .91 .67 .69 4

REC 32 REGI6 REG 6 REG 1 REG 3 REGle REC 23 REG 32 REGIS REG 6 REG 1 REG 3 REGle REG 23 I 1.25 .70 .96 1.e4 1.e4 .84 .57 1.11 .77 1.11 1.18 1.17 .89 .53 REG 31 REGIS REG 5 R$G 4 REC 11 REG 24 REC 31 REGIS REG 5 REG 4 REG 11 REC 24 1.15 1.14 1.59 1.83 1.le 1.44 1.12 1.28 1.85 1.82 1.14 1.26 REG 38 REC 14 REG 13 REG 12 REC 25 REG 38 REG 14 REG 13 REC 12 REC 26

.99 .76 .76 .93 2.31 1.02 .89 .88 .96 1.92

REC 29 REC 28 REG 27 REC 26 REG 29 REG 28 REG 27 REC 26

.51 1.e4 .68 1.27 .54 1.06 .67 1.07 0'

Km 1.8182 Km 1.8998 REGIONS AVG. X DIF. ONE SIGWA X DIFFERENCE i

I - 19 9.38 6.98 REG 35 REC 36 REG 37 REG 2e 4

-18 -2e -17 -16 20 - 37 -8.82 8.27 1 REG 34 REGI8 REC 19 REC 8 REG 21 1 - 37 .87 11.38 -8 e -1 -2 -7 i

REC 33 REG 17 REG 7 REu 2 REG 9 REG 22

-2 9 11 le le e 1

i REC 32 REGI6 REG 8 REG 1 REG 3 RECle REG 23

-11 le 16 14 12 5 -5 I

i REG 31 REGIS REG 5 REG 4 REG 11 REG 24

-2 13 16 11 4 -12 REC 3e REC 14 REGI3 REG 12 REG 25 3 18 17 3 -17 c$

1 REG 29 6

REC 28 2

REC 27

-2 REG 26 [;

-16 os i

DELTA K= .0012 21 i

o

2-D calculctions RPF COWPARISDN FOR TIME POINT EED OF FSV, CYCLE 3

7. PSC CAUCE, TP658, 7-CR00PS AS-BUILT REFLEt. ' IWP. Km 1.8123 i IS COMPARED TO THE REFERENdE CALCULATION :

6. CA BUCTRI, TP658, 7-CROUPS, AS-BUILT REF. IMP., E-4 CONV. Km 1.8103

6. CA BUGTRI, TP658, 7. PSC GAUGE, TP658, REC 35 REC 36 REG 37 REC 2s REC 35 REC 36 REC 37 REC 2e 1.12 1.35 1.83 .96 1.23 1.47 1.89 1.01 REC 34 REC 18 REC 19 REC 8 REC 21 REC 34 REC 18 REC 19 REC 8 REC 21

.91 .89 .94 1.33 1.23 .94 .91 .95 1.34 1.27 4

REC 33 REC 17 REG F REG 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

.85 .83 .8e .82 .75 .89 .83 .88 .78 .88 .73 .98 REC 32 REC 16 REC 6 REC 1 REC 3 RECle REC 23 REC 32 REC 16 REC 6 REC 1 REC 3 REcle REC 23 1.22 .99 .88 .75 .87 1.17 .88 1.28 .94 .83 .72 .83 1.15 .96

]

REC 31 REGIS REC 5 REC 4 REC 11 REC 24 REC 31 REGIS REC 5 REC 4 REC 11 REC 24

.99 1.25 1.28 1.33 1.81 1.e3 .96 1.19 1.14 1.28 lose 1.05 REC 3e REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REC 13 REC 12 REC 25

.92 1.Se .71 1.01 1.37 .91 .96 .68 1.86 1.42 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26

.79 1.11 .89 .89 .8e 1.14 .92 .93 a da M= 1.8183 Km 1.0123

RECIDNS AVC. 5 DIF. ONE SICMA 5 DIFFERENCE 1 - 19 -2.64 2.16 REC 35 REC 36 REC 37 REC 2e

^.

9 9 6 5 l

28 - 37 2.58 3.42 REC 34 REC 18 REC 19 REC 8 REC 21 e 1 - 37 .le 3.85 3 2 1 1 3 2EC33 REC 17 REC 7 REC 2 REC 9 REC 22

, -2 -3 -2 -2 -3 1 i

REC 32 REC 16 REC 6 REC 1 REC 3 REC 18 REC 23 J -2 -5 -5 -5 -4 -1 2 REC 31 REGIS REC 5 REC 4 REC 11 REC 24 i -3 -4 -5 -4 -1 2 J

REC 3e REC 14 REC 13 REC 12 REC 25

-2 -4 -4 -1 4 e i

' O REC 29 REC 28 REC 27 REC 26 j?

j

\

1 3 3 4 w os DELTA Km .8628 g l 25 i

, 2-D calculations RPF COMPARISDN FOR TIME POINT CSS OF FSV, CYCLE D

8. PSC N00AL DIF3D TP 658 7-GROUPS, AS-BUILT REF. IWP. Km 1.9688 IS COMPARED TO THE REFERENCE CALCULATION :

6. CA BUCTRI, TP658, 7-GROUPS, AS-BUILT REF. IMP., E-4 CONY. K= 1.8183

6. GA BUGTRI, TP658, 8. PSC NODAL DIF3D REC 35 REC 36 REC 37 REC 28 REC 36 REC 36 REG 37 REC 2s 1.12 1.35 1.93 .96 1.06 1.29 1.91 .93 REC 34 REGI8 REC 19 REG 8 REC 21 REG 34 REGIS REC 19 REG 8 REG 21

.91 .89 .94 1.33 1.23 .87 .98 .96 1.34 1.18 e

j REC 33 REG 17 REG 7 REG 2 REG 9 REG 22 REG 33 REG 17 REG 7 REG 2 REG 9 REG 22 i

.86 .83 .88 .82 .75 .89 .79 .83 .82 .86 .77 .87 REG 32 REC 16 REG 6 REG 1 REG 3 REGIS REC 23 REC 32 REG 16 REG 6 REG 1 REG 3 REGle REC 23 1.22 .99 .88 .76 .87 1.17 .88 1.99 .98 .90 .79 .91 1.19 .86 i

REC 31 REGIS REG S REG 4 REC 11 REG 24 REG 31 REGIS REG E REG 4 REG 11 REC 24

.99 1.26 1.28 1.33 1.81 1.83 .94 1.25 1.26 1.39 1.06 1.62 REG 38 REG 14 REGI3 REG 12 REG 2b RE638 REC 14 REGIS REG 12 REC 26

.93 1.06 .71 1.61 1.37 .91 1.83 .75 1.86 1.36 REC 29 REC 28 REG 27 REC 26 REG 29 REG 28 REG 27 REG 26

.79 1.11 .89 .89 .78 1.11 .91 .89 03 Km 1.0163 Km 1.6688 i

REGIONS AVG. X OIF. ONE SIGMA X DIFFERENCE 1 - 19 2.79 2.93 REG 36 REG 36 REG 37 REG 20

-6 -4 -2 -3 J 20 - 37 -3.89 2.87 REG 34 REGIS REG 19 REG 8 REG 21 1 - 37 .87 3.85 -5 1 1 1 -4 REC 33 REC 17 REG 7 REG 2 REC 9 REG 22 3 -7 e 3 4 2 -2 REG 32 REGI6 REC 6 REG 1 REG 3 REGIS REC 23 j -11 -1 3 5 5 2 -3 REC 31 REGI6 REG S REG 4 REC 11 REC 24

-6 s S 5 4 -1 REC 3s REG 14 REG 13 REG 12 REG 25

-2 3 6 6 -1 g3 o

REG 29 REC 28 REC 27 REG 26 wo

-1 8 2 8 ((

m DELTA Km .9616 g o

2-D calculations RPF COMPARISDN FOR TIME POINT E5e OF FSV, CYCLE 3

9. PSC 6-TRI/ HEX DIF TP658, 7-CROUPS, AS-BUILT REF. IMP. Km 1.0694 IS COMPARED TO THE REFERENCE CALCULATTON :

6. GA BUGTRI, TP658, 7-GROUPS, AS-BUILT REF. IMP., E-4 CONY. Km 1.6103

6. GA BUGTRI, TP650, 9. PSC 6-TRI/NEX DIF REC 35 REG 36 RE037 REG 2e REC 35 REG 36 REG 37 REC 2s 1.12 1.35 1.83 .96 1.05 1.29 1.es .92 REC 34 REG 18 REC 19 REG 8 REG 21 REG 34 REGIS REG 19 REG 8 REC 21

.91 .89 .94 1.33 1.23 .87 .95 .95 1.34 1.18 REC 33 REC 17 REG 7 REG 2 LEG 9 REC 22 REG 33 REC 17 REC 7 REG 2 REG 9 REG 22

.85 .83 .de .82 .75 .89 .8e .84 .83 .85 .78 .87 REC 32 REC 16 REG 6 REG 1 REG 3 RECle REC 23 REG 32 REGI6 REG 6 REG 1 REG 3 RECle REC 23 1.22 .99 .88 .75 .87 1.17 .88 1.09 .98 .91 .79 .91 1.19 .85 REC 31 REGIS REG 5 REG 4 REG 11 REC 24 REC 31 REGIS REG 5 REG 4 REC 11 REC 24

.99 1.25 1.20 1.33 1.01 1.03 .94 1.26 1.26 1.40 1.95 1.01 REC 38 REC 14 REC 13 REC 12 REG 25 REC 3e REC 14 REGIS REG 12 REC 25

.93 1.00 .71 1,81 1.37 .91 1.e4 .76 1.06 1.33 REC 29 REC 28 REC 27 REC 26 REG 29 REC 28 REC 27 REC 26 y .79 1.11 .89 .89 .78 1.11 .91 .88 s

4)

Km 1.8183 Km 1.0094 RECIONS AVG. X DIF. ONE SIGMA 5 DIFFERENCE 1 - 19 3.36 2.17 REC 35 REC 36 REC 37 REC 28

~ ~ ~ ~

20 - 37 -3.45 2.73 REG 34 REC 18 REC 19 REG 8 REG 21 1 - 37 .62 4.19 -5 1 1 1 -4 REC 33 REC 17 REG 7 REG 2 REG 9 REC 22

-5 1 4 4 4 -2 REC 32 REC 16 REG 6 REG 1 REC 3 REGle REC 23

-11 -1 4 5 5 2 -4 REC 31 REC 15 REG S REG 4 REC 11 REC 24

-5 1 5 5 4 -2 REC 3e REC 14 REGIS REC 12 REC 25

-2 4 8 5 -3 l@

e REC 29 REC 28 REC 27 REC 26 *-

-1 e 2 -2 $(

DELTA Km .8009 $

o i

2-D calculations RPF COMPARISDN FOR TIME POINT ESS OF FSV, CYCLE 3

10. PSC 24-TRI/ HEX DIF TP658 7-GROUPS, AS-BUILT REF. IMP. Km 1.8897 IS COMPARED TO THE REFERENCE CALCUtATION :

6. GA BUCTRI, TP658, 7-GROUPS, AS-BUILT REF. IMP., E-4 CONV. Km 1.6183 6

6. GA BUGTRI, TP658, 18. PSC 24-TRI/ HEX DIF REG 35 REC 36 REC 37 REC 28 REC 35 REC 36 REG 37 REC 2e 1.12 1.35 1.83 .96 1.99 1.32 1.92 .94 REC 34 REC 18 REC 19 REC 8 REC 21 REC 34 REC 18 REC 19 REG 8 REG 21

.91 .89 .94 1.33 1.23 .89 .98 .95 1.33 1.19 4

REC 33 REC 17 REC 7 REC 2 REG 9 REC 22 REC 33 REC 17 REG 7 REG 2 REG 9 REG 22

.85 .83 .80 .82 .75 .89 .81 .83 .81 .84 .77 .87 REG 32 REGI6 REG 6 REG 1 REG 3 REC 16 REC 23 REC 32 REC 16 REG 6 REG 1 REG 3 REcis REG 23 1.22 .99 .88 .75 .87 1.17 .88 1.12 .98 .89 .77 .89 1.18 .87 REC 31 REGIS REG S REG 4 REC 11 REC 24 REC 31 REGIS REG S REG 4 REC 11 REC 24

.99 1.25 1.28 1.33 1.81 1.83 .95 1.25 1.23 1.37 1.e4 1.02 REG 3e REC 14 REG 13 REC 12 REC 25 REC 3s REG 14 REC 13 REG 12 REC 25 2 .93 1.06 .71 1.81 1.37 .92 1.82 .74 1.e4 1.36 REG 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REG 26 y .79 1.11 .89 .89 .79 1.12 .91 .98 e

1

[] K= 1.8183 Km 1.9497 3 REGIONS AVC. 5 DIF. ONE SIGWA X DIFFERENCE 1 - 19 1.89 1.48 REC 35 REC 36 REC 37 REC 2s

-3 -2 -1 -2 l 28 - 37 -1.87 2.38 l REG 34 REGIS REC 19 REG 8 REC 21 1 - 37 .81 2.64 -2 1 1 8 -3 REC 33 REC 17 REG 7 REG 2 REG 9 REC 22

-4 5 1 3 2 -2 REC 32 REC 16 REG 6 REG 1 REG 3 REG 1s REC 23

-8 -1 2 2 3 1 -2 REC 31 REC 15 REQ 5 REG 4 REC 11 REC 24

-4 8 3 3 3 -1 REC 3s REC 14 REC 13 REG 12 REG 25 q,

-1 2 5 3 -1 c3 u)

REC 29 8

REC 28 1

REC 27 2

REC 26 1

((

os DELTA Km .0006 d a

2-D calculations RPF COMPARISDN FOR TIME POINT (Se DF FSV, CYCLE 3

8. PSC N00AL DIF3D TP 658 7-GROUPS, AS-BUILT REF. IMP. Km 1.9888 IS CGWPARED TO THE REFERd.NCE CALCULATION :

7. PSC GAUGE, TP658, 7-GROUPS, AS-BUILT REFLECTOR IMP. K= 1.8123

7. PSC CAUCE, TP658, 8. PSC NODAL DIF30 REC 35 REC 36 REC 37 REC 2a REC 35 REG 36 REC 37 REG 2s 1.23 1.47 1.99 1.01 1.86 1.29 1.01 .93 REC 34 REGI8 REG 19 REG 8 REG 21 REC 34 REC 18 REG 19 REG 8 REC 21

.94 .91 .95 1.34 1.27 .87 .98 .95 1.34 1.18 REC 33 REC 17 REG 7 REC 2 REG 9 REC 22 REC 33 REG 17 REG 7 REG 2 REG 9 REC 22

.83 .88 .78 .88 .73 .98 .79 .83 .82 .85 .77 .87 REC 32 REC 16 REG 6 REG 1 REG 3 REGle REG 23 REC 32 REGlo REG 6 REG 1 REG 3 REGle REC 23 1.20 .94 .83 .72 .83 1.15 .98 1.89 .98 .98 .79 .91 1.19 .86 REC 31 REGIS REG E REG 4 REC 11 REG 24 REC 31 REGIS REC 5 REG 4 REG 11 REC 24

.96 1.19 1.14 1.28 1.98 1.85 .94 1.25 1.25 1.39 1.06 1.92 REG 3s REC 14 REGIS REC 12 RE^25 REC 38 R5G14 REGIS REG 12 REG 25

.91 .96 .68 1.08 1.42 .91 1.83 .76 1.06 1.35 REG 29 REG 28 REC 27 REG 26 REC 29 REC 28 REG 27 REG 26

.63 1.14 .92 .93 .78 1.11 .91 .89

Km 1.8123 Km 1.6088 REGIONS AVG. 5 DIF. ONE SIGMA X DIFFERENCE 1 - 19 5.63 3.42 REC 35 REC 36 REC 37 REC 2e

-14 -12 -7 -8 28 - 37 -5.45 3.74 REC 34 REG 18 REG 19 REG 8 REC 21 1 - 37 .24 6.63 -7 -1 e e -7 REC 33 REG 17 REG 7 REG 2 REG 9 REC 22

-5 4 5 6 5 -3 REC 32 REC 16 REG 6 REG 1 REG 3 NEGIS REC 23

-9 4 8 IS le 3 -4 REC 31 REGIS REG S REG 4 REC 11 REC 24

-2 5 IS 9 5 -3 REC 3e REC 14 REC 13 REG 12 REC 25 3 7 18 6 -5 us o

REG 20 REC 28 REG 27 REG 26 j!

-2 -3 -1 -4 to o

DELTA K= .8835 :c E

2-D calculctions RPF COMPARISON FOR TIME POINT 4:50 OF FSV, CYCLE 3

6. CA BUGTRI TP658 7-CROUPS, AS-BUILT REF. IMP., E-4 CONY. K= 1.81e3 IS COMPANEp TO YHE REFERENCE CALCULATION :

12. CA'WEASURED VALUES, TP658, CALCULATED BY FSVCORE K= 1. sees 4

12. CA MEASURE 8 VALUES 6. GA BUCTRI, TP658, REC 35 REC 36 REC 37 REC 2s REC 35 REC 36 REC 37 REG 2e 1.29 1.34 1.01 1.se 1.12 1.35 1.83 .96 RE634 REC 18 REC 19 REC 8 REC 21 REC 34 REC 18 REC 19 REC 8 REC 21

.87 .S2 1.06 1.34 .97 .91 .89 .94 1.33 1.23 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

.78 .83 .88 .92 .75 .72 .85 .83 .88 .82 .75 .89

REC 32 REC 16 REC c REC 1 REC 3 RECle REC 23 REC 32 REGIS REC 6 REC 1 RE9 3 REcle REC 23

1.19 1.83 .96 .88 .96 1.19 .75 1.22 .99 .88 .75 .87 1.17 .88

< REC 31 REGIS REC 5 REC 4 REC 11 REC 24 REC 31 REGIS REC 5 REC 4 REC 11 REC 24

.88 1.26 1.25 1.39 1.99 .93 .90 1.25 1.2e 1.33 1.01 1.83 REC 38 REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REC 13 REC 12 REC 25

.87 1.89 .79 1.11 1.27 .93 1.es .71 1.01 1.37 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26 p .82 1.e4 .87 .82 .79 1.11 .89 .89 8

g Km 1.eees Km 1.8193 REGIONS AVC. X DIF. ONE SICMA X DIFFERENCE 1 - 19 -5.86 4.33 REC 35 REC 36 REC 37 REC 2e

-6 e 2 -3 2e - 37 7.22 8.83 REC 34 REdle REC 19 REC 8 REC 21 1 - ?,7 .Se 9.49 5 -4 -6 e 26 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 9 e -9 -11 1 24 REC 32 REC 16 REC 6 REC 1 REC 0 REC 19 REC 23 3 -4 -9 -14 -le -2 18 REC 31 REGIS REC 5 REC 4 REC 11 REC 24 13 -1 -4 -4 -7 11 REC 3e REC 14 REGI3 REC 12 REC 25 6 -9 -le -9 8 y REC 29 REC 28 REC 27 REC 26 8'

-3 7 3 9 $

DELTA Km .5183 23 o

2-D calculations RPF COMPARISDN FOR TIME POINT SES OF FSV, CYCLE 3

7. PSC CAUCE, TP650 7-CRDUPS, AS-BUILT REFLECTOR IMP. Km 1.9123 IS COMPARED TO YHE *tEFERENCE CALCULATION :

12. CA WEASURED VALUES, TP658, CALCULATED BY FSVCORE Km 1. Sees

12. GA WEASURED VALUES 7. PSC GAUCE, TP658, REG 35 REC 36 REC 37 REC 2e REC 36 REC 36 REC 37 REG 2e 1.20 1.34 1.81 1.Se 1.23 1.47 1.69 1.01 i

REC 34 REGIS REC 19 REC 8 REC 21 REG 34 REGIS REGI9 REG 8 REG 21

.87 .92 1.Se 1.34 .97 .94 .91 .95 1.34 1.27 j REC 33 REG 17 REG 7 REG 2 CEG 9 REC 22 REG 33 REC 17 REC 7 REG 2 REG 9 REC 22

.73

.78 .83 .88 .92 .76 .72 .83 .88 .78 .88 .98 REC 32 REC 16 REG 6 REG 1 REC 3 REGle REC 23 REC 32 REG 18 REG 8 REG 1 REC 3 RECle REC 23 1.19 1.83 .96 .88 .96 1.19 .75 1.28 .94 .83 .72 .83 1.15 .98 REG 31 REC 15 REG 5 REG 4 REC 11 REG 24 REC 31 REGIS REG S REG 4 REC 11 REC 24

.88 1.26 1.25 1.39 1.99 .93 .96 1.19 1.14 1.28 1.86 1.85 REC 3e REG 14 REC 13 REC 12 REC 25 REC 30 REG 14 REG 13 REC 12 REC 26

) .87 1.89 .79 1.11 1.27 .91 .96 .68 1.Se 1.42 REC 29 REC 28 REC 27 REC 26 REC 29 REG 28 REC 27 REC 26

. .82 1.e4 .87 .82 .8e 1.14 .92 .93

[ Km 1.0806 Km 1.6123 RECIONS AVG. X DIF. ONE SIGMA X DIFFERENCE 1 - 19 -8.33 5.94 REC 35 REG 36 REC 37 REC 2s 3 9 8 1 20 - 37 9.87 8.38 REC 34 REC 18 REC 19 REC 8 REC 21 1 - 37 .52 11.44 8 -1 -S S 31

, REC 33 REC 17 REG 7 REG 2 REG 9 REC 22 7 -3 -11 -13 -2 26 REC 32 REGIS REG 6 REC 1 REG 3 REGle REC 23 1 -9 -14 -18 -14 -3 28 REC 31 REGIS REG 6 REC 4 REG 11 REC 24 9 -6 -9 -8 -8 13 REC 38 REC 14 REG 13 REG 12 REC 26 4 -12 -14 -le 12 pg REC 29 REC 28 REC 27 REG 26 )$

-2 le 6 13 {$

DELTA Km .9123  ::

E

2-D calculctions RPF COMPARISON FOR TIWE POINT CSS OF FSV, CYCLE 3

8. PSC NODAL DIF3D TP 659 7-GRDUPS, AS-BUILT REF. IWP. K= 1.SeE8 IS CouPARED TO THE REFERdNCE CALCULATION :

12. CA MEASURED VALUES, TP656, CALCULATED BY FSVCORE K= 1. sees

12. CA MEASURED VALUES 0. PSC NODAL DIF3D REC 35 REC 36 REC 37 REC 2e REG 35 REC 36 REC 37 REG 2e 1.28 1.34 1.81 1.00 1.06 1.29 1.01 .93 REC 34 REC 18 REGI9 REG 8 REC 21 REC 34 REG 18 REG 19 REG S REG 21

, .87 .92 1.06 1.34 .97 .87 .96 .95 1.34 1.18 REC 33 REC 17 REC 7 REG 2 REG 9 REC 22 REC 33 REG 17 REG 7 REG 2 REG 9 REC 22

.78 .83 .88 .92 .75 .72 .79 .83 .82 .86 .77 .87

! REC 32 REC 16 REG 6 REG 1 REG 3 REC 16 REC 23 REC 32 REC 16 REG 6 REG 1 REG 3 REGle REC 23 1.19 1.03 .96 .88 .96 1.19 .75 1.89 .98 .98 .79 .91 1.19 .86 REC 31 REC 15 REG 5 REC 4 REG 11 REC 24 REC 31 REC 15 REG E REG 4 REC 11 REC 24

.88 1.26 1.25 1.39 1.99 .93 .94 1.25 1.25 1.39 1.85 1.92 REC 3s REC 14 REG 13 REG 12 REC 25 REC 3e REC 14 REGIS REC 12 REC 25 a

i .87 1.89 .79 1.11 1.27 .91 1.83 .75 1.06 1.35 REC 29 REC 28 REG 27 REC 26 REC 29 REC 28 REC 27 REC 28

, > .82 1.e4 .97 .82 .78 1.11 .91 .89 s

7 Km 1.000s Km 1.0088 1 REGIONS AVG. X DIF. ONE SICMA X DIFFERENCE 1 - 19 -3.38 3.44 REG 35 REC 36 REC 37 REC 2e

-11 -4 e -7 28 - 37 3.92 9.22 REC 34 REGIS REC 19 REG 8 REC 21 1 - 37 .21 7.71 e -2 -5 e 21 REC 33 REG 17 REG 7 REG 2 REG 9 REC 22 2 1 -6 -8 3 21 REC 32 REC 16 REG 6 REG 1 REG 3 RECIS REC 23

-8 -5 -6 -le -6 8 14 REC 31 REC 15 REG S REC 4 REC 11 REC 24 7 -1 e 8 -4 9 w>

REC 3e REC 14 REC 13 REG 12 REC 25 c) 4 -6 -5 -5 6 jR

!' u REC 29 REC 28 REC 27 REC 26 0'

-4 7 4 9 z DELTA Km .0088 O I

2-D calculctions RPF COMPARISDN FOR TIME POINT CSS OF FSV, CYCLE 3

9. PSC 6-TRI/ HEX DIF TP650, 7-CR00PS, AS-BUILT REF. IWP. Km 1.0094 IS C0c ARED TO THE REFERENCE CALCULATION :

12. CA WEASURED VALUES, TP658, CALCULATED BY FSVCORE Km 1.900s

12. CA MEASURED VALUES 9. PSC 6-TRI/ HEX DIF REC 35 REC 36 REC 37 REC 2e REC 35 REC 36 REC 37 REC 2e 1.28 1.34 1.01 1.06 1.95 1.29 1.se .92 REG 34 REGIS REC 19 REC 8 REC 21 REJ34 REC 18 REC 19 REG 8 REC 21

.87 .92 lose 1.34 .97 .87 .9e .95 1.34 1.18 REC 33 REC 17 REG 7 REG 2 NEG 9 REC 22 REC 33 REC 17 REG 7 REG 2 REG 9 REC 22

.78 .83 .88 .92 .75 .72 .88 .84 .83 .85 .78 .87 REC 32 REGlo REG 6 REG 1 REG 3 REC 18 REC 23 REC 32 REC 16 REG 6 REG 1 REG 3 REGle REC 23 1.19 1.03 .96 .P9 .96 1.19 .75 1.e9 .98 .91 .79 .91 1.19 .85

]

REC 31 REGIS REC 5

• EG 4 REC 11 REC 24 REG 31 REGIS REG 5 PEG 4 REC 11 REC 24

.88 1.26 1.25 1.39 1.89 .93 .94 1.26 1.26 1.48 1.85 1.01 REC 3e REC 14 REGIS REC 12 REC 25 REC 3e REC 14 REC 13 REC 12 REC 25

.87 1.09 ,79 1.11 1.27 .91 1.e4 .76 1.06 1.33 REC 29 REG 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26

.82 1.e4 .87 .82 .78 1.11 .91 .88 y Km 1.0006 Km 1.9694 L

REGIONS AVQ. X DIF. ONE SICMA X DIFFERENCE 1 - 19 -2.81 3.64 REC 35 REC 36 REC 37 REC 2e

-12 -4 -1 -8 20 - 37 3.54 9.22

' REC 34 REGIS REC 19 REC 8 REC 21 1 - 37 .28 7.56 8 -2 -5 e 21 REC 33 REC 17 REG 7 REC 2 REG 9 REC 22 3 2 -5 -8 4 21 REC 32 REGIS REC 6 REC 1 REC 3 RECle REC 23 2

-8 -5 -5 -le -6 8 13 REC 31 REGIS REG S REG 4 REC 11 REC 24 7 e 1 1 -4 8 i REC 3e REC 14 REC 13 REC 12 REC 25 l 4 -5 -4 -5 5 REC 29 REC 28 REC 27 REC 26 u)

-4 7 4 7 8 DELTA Km .0094 yl E

n

2-D calculations RPF COMPARISON FOR TIME POINT CSS OF FSV, CYCLE 3 le. PSC 24-TRI/ HEX DIF TP658 7-CROUPS, AS-BUILT REF. IMP. K= 1.0097 IS COMPARED TO THE REFERdNCE CALCULATION :

12. CA MEASURED VALUES, TP658, CALCULATED BY FSVCORE Km 1. sees

12. GA MEASURED VALUES 18. PSC 24-TRI/ HEX DIF REC 35 REG 36 REC 37 REC 28 REC 35 REC 36 REG 37 REC 2s 1.28 1.34 1.01 1.00 1.09 1.32 1.02 .94 REC 34 REGIS REC 19 REG 8 REC 21 REC 34 REC 18 REC 19 REG 8 REC 21

.87 .92 1.se 1.34 .97 .89 .98 .95 1.33 1.19 REG 33 REC 17 REG 7 REG 2 REG 9 REC 22 REG 33 REC 17 REG 7 REG 2 REG 9 REC 22

.78 .83 .88 .92 .75 .72 .81 .83 .81 .84 .77 .87 REC 32 REC 16 REG 6 REC 1 REG 3 RECle REC 23 REG 32 REC 16 REG 6 REG 1 REG 3 REGis REG 23 1.19 1.83 .96 .88 .96 1.19 .75 1.12 .98 .89 .77 .89 1.18 .87 REC 31 REGIS REG E REG 4 REC 11 REC 24 REC 31 REC 15 REG 5 REG 4 REG 11 REC 24

.88 1.26 1.25 1.39 1.09 .93 .95 1.25 1.23 1.37 1.e4 1.82 REC 3e REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REGIS REC 12 REC 25

.87 1.09 .79 1.11 1.27 .92 1.02 .74 1.e4 1.36 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26

.82 1.e4 .87 .82 .70 1.12 .91 .96 I Km 1.0006 Km 1.0097 RECIONS AVG. X DIF. DNE SICMA X DIFFERENCE 1 - 19 -4.28 3.84 REC 35 REC 36 REC 37 REC 2e

~ ~ ~

28 - 37 5.19 8.74 REC 34 REC 18 REC 19 REC 8 REC 21 1 - 37 .37 8.13 2 -2 -5 -1 22 REC 33 REC 17 REC 7 REG 2 REG 9 REC 22 4 1 -7 -9 3 21 REC 32 REC 16 REG 6 REG 1 REC 3 RECle REC 23

-6 -5 -7 -12 -8 -1 16 REC 31 REGIS REG 5 REG 4 REC 11 REC 24 8 -1 -1 -1 -5 9 REC 38 REC 14 REC 13 REC 12 REC 25 5 -6 -6 -7 7 e o

REC 29 REC 28 REC 27 REC 26 $3

-3 8 4 IS ga DELTA K= .9997 :2:

E

2-D calculctions RPF COMPARISON FOR TI E P3 INT CSS OF FSV, CYCLE 3 I

?

11. PSC MEASURED VALUES, TP65s calculated by POKE K= 1.eees

IS COMPARED TO THE REFERENCE CALCULATION

j 12. GA MEASURED VALUES, TP658, CALCULATED BY FSVCORE Km 1.8000 1

12. CA MEASURED VALUES 11. PSC MEASURED VALUE

, REC 35 REC 36 REC 37 REC 2e REG 35 REC 36 REC 37 REC 2e 1.20 1.34 1.01 1.88 1.22 1.31 .99 1.81

{

REC 34 REC 18 REC 19 REG 8 REC 21 REC 34 REC 18 REC 19 REC 8 REC 21

.87 .92 1.Se 1.34 .97 .84 .93 1.06 1.34 .98 REC 33 REG 17 REG 7 REG 2 KEG 9 REC 22 REG 33 REG 17 REG 7 REG 2 REG 9 REC 22

.78 .83 .88 .92 .75 .72 .75 .83 .88 .93 .75 .71 REC 32 REC 16 REG 6 REG 1 REG 3 RECle REG 23 REC 32 REC 16 REO 6 REG 1 REG 3 REcle REC 23 1.19 1.93 .96 .88 .96 1.19 .75 1.11 1.e4 .97 .88 .97 1.19 .76 REG 31 REC 15 REC 6 RF' 4 REC 11 REG 24 REG 31 REGIS REC 6 REG 4 REC 11 REC 24

.88 1.26 1.25 ". 39 1.09 .93 .88 1.27 1.25 1.39 1.le .94 REC 3s REC 14 REGIS REC 12 REC 25 REG 3e REG 14 REGIS REG 12 REG 25 l .87 1.99 .79 1.11 1.27 .88 1.10 .79 1.12 1.28 l

j REC 29 REC 28 RFC27 REC 26 REG 29 REC 28 REC 27 REC 26

.82 1.e4 .87 .82 .82 1.e4 .88 .82 y Km 1.0006 Km 1.0000 i

RECIONS AVG. X DIF. ONE SIGMA X DIFFERENCE i

$ 1 - 19 .59 .29 REC 35 REC 36 REC 37 REC 2e j 2 -3 -2 1 1 28 - 37 .55 2.23 REC 34 REGIS REC 19 REG 8 REC 21 1 - 37 .84 1.65 -3 1 e e 1 FEC33 REC 17 REC 7 REC 2 REC 9 REG 22

-3 1 1 1 w -1 1

REC 32 REGlo REG 6 REC 1 REG 3 RECle REC 23

-7 1 1 1 1 e 1 l REC 31 REGIS REG S REC 4 REG 11 REC 24 e 1 e e 1 1 REC 3e REC 14 REGIS REC 12 REG 25 y3 a 1 1 e 1 1 c) e REC 29 8

REC 28 e

REC 27 1

REC 26 e

[l os DELTA Km .0000 do j

909436 N/C

,. APPENDIX B THREE-DIMENSIONAL RADIAL PEAKING FACTOR COMPARISONS FOR CYCLE 3 F

4 B-1

RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 3

21. GA DIF3D, 3/28 CYC.3/178.4 EFPD, 4-CRPS, AS-BUILT REF. IMP. M= 1.8345 IS COMPARED TO THE REFERENCE CALCULATION :

8. GA CATT, 3/20 CYC.3/178.4 EFPD, 4-GRPS, AS-BUILT REF. IW?. Km 1.034f

8. GA GATT, 3/28 C 21. GA DIF3D, 3/28 C REC 35 REC 36 REC 37 REC 2e REC 35 REC 36 REC 37 REC 28 1.38 1.62 1.21 .93 1.17 1.39 1.99 .85 REG 34 REGI8 REC 19 REC 8 REC 21 REC 34 REGIS REG 19 REC 8 REC 21

.96 .92 .88 1.26 .68 .87 .89 .88 1.26 .66 REG 33 REG 17 REG 7 REC 2 REG 9 REC 22 REC 33 REG 17 REG 7 REG 2 REG 9 REG 22

.54 .82 .96 .96 .68 .75 .53 .86 1.92 1.83 .74 .73 REG 32 REC 16 REC 6 REG 1 REC 3 REGle REC 23 REC 32 REG 16 REG 6 REG 1 REC 3 RECle REG 23 1.12 .99 1.93 .96 .97 1.e4 .92 1.06 1.e4 1.13 1.85 1.06 1.88 .87 REG 31 REGIS REG 5 REG 4 REC 11 REC 24 REC 31 REGIS REG S REG 4 REC 11 REC 24 1.e4 1.e4 1.35 1.51 .91 1.13 1.92 1.11 1.49 1.64 .97 1.99 REG 38 REG 14 REG 13 REG 12 REC 25 REC 3e REG 14 REC 13 REC 12 REG 26

.96 .92 .69 1.06 1.51 .95 .99 .77 1.13 1.43 REC 29 REC 28 REG 27 REC 26 REC 29 REG 2d REG 27 REG 26 os .82 1.81 .58 .92 .Se 1.81 .59 .88 K= 1.0345 K= 1.8345 REGIONS AVC. X DIF. ONE SICWA X DIFFERENCE 1 - 19 6.24 3.85 REG 36 REC 36 REG 37 REG 2e

-16 -14 -18 -9 20 - 37 -5.14 4.75 REC 34 REGIS REC 19 REG 8 REG 21 1 - 37 .78 7.17 -9 -3 6 8 -2 REC 33 REC 17 REG 7 REC 2 REC 9 REC 22

-2 5 6 7 8 -2 REC 32 REGI6 REC 6 REC 1 REC 3 REGIS REG 23

-6 5 le 9 le 4 -5 REC 31 REGI6 REG 6 REG 4 REG 11 REG 24

-2 7 le 9 7 -4 REC 3e REC 14 REC 13 REC 12 REC 25

-1 7 12 7 -5 w>

O REC 29 REC 28 REG 27 REC 26 W)

-3 8 2 -4 [l m

DELTA Km .0000 g 25

RPF COWPARISON FOR 3D CALCULATIONS, FSV CYCLE.3

22. Ca DIF3D, 3/21 CYC.3/188.8 EFPD, 4-49PS, AS-BUILT REF. IWP. Km 1.0856 IS COMPARED TO THE REFERENCE CALCULATION :

9. GA GATT, 3/21 CYC.3/188.8 EFPD, 4-GRPS, AS-BUILT REF. IMP. Km 1.Se56

9. GA CATT, 3/21 C 22. GA DIF3D, 3/21 C REC 35 REC 36 REC 37 REC 2s REG 35 REC 36 REC 37 REG 28 1.36 1.68 1.28 .94 1.22 1.45 1.14 .89 REG 34 REGIS REG 19 REG 8 REC 21 REC 34 REGIS REC 19 REC 8 REC 21

.96 .90 .87 1.27 .71 .91 .98 .98 1.31 .71 REG 33 REG 17 REC 7 REG 2 REC 9 REC 22 REG 33 REG 17 REG 7 REG 2 REC 9 REG 22

.55 .82 .93 .94 .69 .77 .55 .87 .99 1.00 .75 .76 REC 32 REGlo REG 6 REC 1 REG 3 REGle REG 23 REC 32 REGI6 REC 6 REG 1 REC 3 REGle REC 23 1.16 .99 1.81 ,93 .96 1.e4 .92 1.98 1.83 1.88 .99 1.02 1.07 .88 REC 31 REGIS REC 5 REC 4 REG 11 REC 24 REC 31 REGIS REC 6 REG 4 REG 11 REC 24 1.06 1.05 1.33 1.48 .98 1.13 1.82 1.le 1.42 1.57 .95 1.88 REC 3e REG 14 REGIS REG 12 REG 25 REC 3e REC 14 REC 13 REC 12 REC 25

.97 .93 .78 1.06 1.51 .95 .97 .76 1.11 1.43 REG 29 REC 28 REC 27 REG 26 REC 29 REG 28 REG 27 REC 26 o, .84 1.85 .68 .93 .Se 1.92 .68 .88 s

Km 1.0856 Km 1.0056 l

l REGIONS AVG. % DIF. ONE SIGWA  % DIFFERENCE 1 - 19 5.26 1.95 REC 35 REC 36 REC 37 REC 2e

-11 -9 -5 -5 28 - 37 -4.28 3.82 REG 34 REC 18 REG 19 REC 8 REC 21 1 - 37 .66 5.41 -6 e 3 3 e REC 33 REC 17 REG 7 REC 2 REC 9 REC 22 1 6 6 7 8 -2 REC 32 REC 16 REG 6 REG 1 REG 3 REGle REG 23

-7 5 7 6 7 3 -5 REG 31 REC 15 REG S REC 4 REC 11 REC 24

-3 5 7 6 6 -4 REC 38 REG 14 REG 13 REG 12 REC 25 pj

-2 4 8 4 -6 q) s~

REC 29 REC 28 REC 27 REC 26 I$

-5 -3 0 -5

'A DELTA Km . Sees 3 u .

3 ,

RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 3

23. CA DIF3D, 3/22 CYC.3/168.5 EFPD, 4-GRPS, AS-BUILT REF IMP. K= 1.0179 IS COMPARED TO THE REFERENCE CALCULATION :

18. GA GATT, 3/22 CYC.3/188.5 EFPD, 4-GRPS, AS-BUILT REF. IWP. Km 1.0198

10. GA GATT, 3/22 C 23. CA DIF3D, 3/22 C REC 35 REC 36 REG 37 REG 2e REC 35 REC 36 REC 37 REG 2e 1.31 1.42 1.18 1.86 1.19 1.35 1.15 1.06 REC 34 REC 18 REC 19 REG S REC 21 REG 34 REGIS REC 19 REG S REC 21 1.87 . 14 5 .79 1.31 1.26 .97 .96 .85 1.48 1.29 REC 33 REC 17 REC 7 REG 2 REC 9 REC 22 REC 33 REC 17 REC 7 REG 2 REC 9 REC 22

.94 .87 .83 .83 .76 .94 .79 .85 .87 .91 .84 .98 REC 32 REGIS REC 6 REC 1 REG 3 RECis REC 23 REG 32 REG 16 REG 6 REC 1 REC 3 REGle REC 23 1.27 1.85 .87 .76 .84 1.14 .93 1.86 .96 .91 .81 .92 1.23 .94 REC 31 REGIS REG 5 REC 4 REC 11 REC 24 REC 31 REGIS REG 5 REG 4 REC 11 REC 24

.97 .95 1.14 1.24 .79 1.se .89 .96 1.21 1.33 .86 1.82 REC 38 REG 14 REG 13 REC 12 REC 25 REG 3e REC 14 REC 13 REC 12 REC 25

.89 .98 .69 1.01 1.38 .86 1.01 .74 1.85 1.28 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REG 27 REC 26 m .84 1.25 .93 .94 .Se 1.15 .91 .91 8

8' K= 1.0198 K= 1.8179 REGIONS AVC. X DIF. DNE SIGMA  % DIFFERENCE 1 - 19 5.25 4.03 REC 35 REC 36 REC 37 REC 2e

-9 -5 e e 2e - 37 -4.18 5.87 REC 34 REGIS REC 19 REC 8 REC 21 1 - 37 .78 6.84 -9 1 7 7 2 REC 33 REC 17 REG 7 REC 2 REC 9 REC 22

-16 -2 5 9 11 4 REG 32 REG 16 REC 6 REG 1 REC 3 RECle REC 23

-16 -4 4 7 le 8 1 REG 31 REC 15 REC 5 REC 4 REC 11 REC 24

-8 1 6 7 9 2 REC 3s REC 14 REGI3 REC 12 REG 25

-4 3 7 4 -2 yl REC 29 REG 28 REC 27 REC 26 8'

-5 -4 -2 -4 $(

DELTA Km .0619 $

o

RPF COMPARISDN FOR 3D CALCULATIONS, FSV CYCLE 3 24 GA DIF30, 3/23 CYC.3/20s.e EFPD, 4-CRPS, AS-BUILT REF. IMP. Km 1.0826 IS COMPARED TO THE REFERENCE CALCULATION :

11. GA GATT, 3/23 CYC.3/200.5 EFPD, 4-CRPS, AS-BUILT REF IMP. Km 1.ee4s

31. CA GATT, 3/23 C 24. GA DIF3D, 3/23 C REC 35 REC 36 REC 37 REC 2s REC 35 REC 36 REC 37 REG 2e 1.31 1.47 1.12 1.66 1.18 1.34 1.e4 .97 REG 34 REC 18 REC 19 REG S REG 21 REC 34 REC 18 REC 19 REG 8 REC 21 1,81 .95 .81 1.33 1.24 .96 .94 .82 1.31 1.16 REC 33 REC 17 REG 7 REC 2 REG 9 REC 22 REG 33 REC 17 REC 7 REG 2 RGG 9 REC 22 j .88 .82 .82 .84 .77 .95 .86 .87 .87 .88 .79 .98 REG 32 REC 16 REG 6 REG 1 REG 3 REGle FEC23 REC 32 REC 16 REG 6 REG 1 REC 3 REC 1s REG 23 1.17 .94 .85 .76 .86 1.17 .95 1.13 1.6e .94 .83 .92 1.17 .89 REG 31 REGIS REG 5 REG 4 REC 11 REC 24 REC 31 REG 15 REG S REG 4 REC 11 REC 24

.94 .95 1.16 1.28 .83 1.85 .95 1.82 1.27 1.38 .88 1.81 i REC 3s REC 14 RE413 REC 12 REG 25 REC 3s REC 14 REC 13 REG 12 REC 25 -

l .89 .99 . .' 1 1.02 1.38 .96 1.85 .77 1.87 1.32 REC 29 REG 29 REC 27 REG 26 REC 29 REC 28 REC 27 REC 26

.84 1.28 .92 .96 .83 1.10 .92 .93 dn K= 1.se4s Km 1.0826 REGIONS AVG. X DIF. DNE SICMA X DIFFERENCE 1 - 19 5.42 3.39 REC 35 REC 36 REC 37 REC 2s

-le -9 -7 -8 i 28 - 37 -4.08 3.48 REC 34 REC 18 REC 19 REC 8 REC 21 1 - 37 .8e 5.89 -5 -1 2 -1 -6 REG 33 REC 17 REG 7 REG 2 REC 9 REC 22 e 6 6 5 3 -6 REC 32 REC 16 REC 6 REC 1 REG 3 REGle REC 23

-4 6 le 9 7 8 -7 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 1 8 18 8 5 -4 REC 3e REC 14 REGIS REC 12 REG 25 q) 1 6 8 5 -4 o v)

REC 29 REC 28 RFC27 REC 26 [$

-1 -1 e -4 os DELTA Km .8614 k o

RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 3

25. CA DIF3D, 3/24 CYC.3/20s.s EFPD, 4-CRPS, AS-BUILT REF. IWP. Km 1.814e IS COMPARED TO THE REFERENCE CALGJLATION :

12. C?. CATT, 3/24 CYC.3/20s.s EFPD, 4-GRPS, AS-BUILT REF. IMP. Km 1.8159

12. CA CATT, 3/24 C 25. CA DIF3D, 3/24 C REC 35 REC 36 REC 37 REC 2s REC 35 REC 36 REC 37 REC 2e 1.14 1.37 1.18 1.82 1.06 1.27 1.83 .93 REC 34 REC 18 REC 19 REC 8 MEC21 REC 34 REC 18 REC 19 REC 8 REC 21

.89 .88 .95 1.31 1.25 .88 .9e .96 1.28 1.25 RECa3 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REG 2 REC 9 REC 22

. '< 8 .77 .81 .84 .75 .90 .88 .83 .86 .88 .76 .84 REC 32 REC 16 REC 6 REC 1 REC 3 REC 13 REC 23 REC 32 REG 1S REC 6 REC 1 REC 3 RECle REC 23 1.18 .94 .87 .77 .88 1.16 .91 1.18 1.03 .95 .83 .92 1.16 .84 REC 31 REC 15 REC 5 REG 4 REC 11 REC 24 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24

.95 1.15 1.17 1.31 1.83 1.87 .99 1.25 1.27 1.39 1.06 1.02 REC 3e REG 14 REC 13 REC 12 REC 25 REC 3e REC 14 REC 13 REC 12 REC 25

.91 .98 .78 1.06 1.48 .94 1.05 .75 1.89 1.32 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26

, .88 1.13 .95 .96 .79 1.11 .93 .91 e

os K= 1.0159 Km 1.814e REGIONS AVC. 5 DIF. ONE SICWA X DIFFERENCE 1 - 19 4.94 3.44 REC 35 REC 36 REC 37 REC 2e

-7 -7 -7 -9 20 - 37 -3.52 4.25 REC 34 REGIS REC 19 REC 8 REC 21 1 - 37 .83 5.72 -1 2 1 -2 -8 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 3 7 7 4 1 -7 REC 32 REGIS REC 6 REC 1 REC 3 REGIS REC 23 6 9 9 8 5 8 -7 REC 31 REGIS REC 6 REC 4 REC 11 REC 24 4 9 9 6 3 -5 REG 3e REC 14 REC 13 REC 12 REC 25 u>

4 7 7 3 -6 Cg REC 29 REG 28 REC 27 REC 26 s$

-1 -1 -2 -5 o'

2:

DELTA Km .0019 g

RPF COMPARISDN FOR 3D CALCULATIONS, FSV CYCLE 3

26. CA DIF3D, 3/25 CYC.3/221.8 EFPD, 4-GRPS, AS-BUILT REF. IMP. Km 1.0684 IS CouPARED TO THE REFERENCE CALCULATION :

13. CA CATT, 3/2ts CYC.3/221.8 EFPD, 4-CRPS, AS-BUILT REF. IMP. K= 1.8099

13. CA CATT, 3/25 C 26. CA DIF30, 3/25 C REC 35 REC 36 NEC37 REC 28 REG 35 REC 36 REC 37 REC 2e j 1.22 1.45 1.12 1.83 1.13 1.37 1.18 1.01 REC 34 REC 18 REC 19 REC 8 REC 21 REC 34 REC 18 REC 19 REC 8 REC 21

.95 .92 .95 1.34 1.27 .91 .94 .99 1.38 1.25 REC 33 REC 17 REC 7 REC 2 REG 9 REC 22 REG 33 REC 17 REC 7 REC 2 REC 9 REC 22

.83 .81 .82 . 84 .75 .89 .86 .83 .86 .89 .88 .89 REC 32 REC 16 REC 6 REC 1 REC 3 REC 10 REC 23 REC 32 REC 16 REC 6 RCC 1 REC 3 RECle REC 23 1.16 .97 .87 .76 .85 1.12 .88 1.87 .98 .91 .88 .91 1.17 .86 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 REC 31 REGIS REC 5 REC 4 REC 11 REC 24

.96 1.14 1.15 1.28 .97 1.01 .93 1.17 1.22 1.36 1.82 1.81 REC 3e REC 14 REC 13 REC 12 REC 25 REC 38 REC 14 REC 13 REC 12 REC 25

.96 .97 .69 1.82 1.35 .88 .99 .72 1.85 1.31 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26 es .79 1.12 .92 .93 .75 1.87 .96 .89 Km 1.8699 Km 1.0084 RECIONS AVC. X DIF. DNE SIGMA X DIFFERENCE 1 - 19 4.44 1.8e REC 35 REC 36 REC 37 REC 2e

-7 -5 -2 -2 2e - 37 -3.39 1.97 REC 34 REC 18 REC 19 REC 8 REC 21 1 - 37 .63 4.38 -4 2 4 3 -2 I REG 33 REC 17 REC 7 REC 2 REC 9 REC 22

-4 3 5 6 6 e REC 32 REC 16 REC 6 REC 1 REC 3 RECle REC 23

-7 1 5 6 8 5 -2 REC 31 REGIS REC 6 REC 4 REC 11 REC 24

-3 3 6 6 5 e REC 38 REC 14 REC 13 REC 12 REC 25 y)

-3 2 6 3 -3 g>

REC 29 REC 28 REC 27 REC 26

-5 -4 -3 -4 2:

DELTA K= .0015 }$

RPF COWPARISDN FOR 3D CALCULATIONS, FSV CYCLE 3

27. GA DIF3D, 3/26 CYC.3/221.s EFPD, 4-CRPS, AS-BUILT REF. IWP. Km 1.0083 IS COMPARED TO THE REFERENCE CALCULATION :

14. CA GATT, 3/26 CYC.3/221.0 EFPD, 4-GRPS, AS-BUILT REF. IMP. Km 1.0097

14. CA CATT, 3/26 C 27. CA DIF3D, 3/26 C REC 35 REC 36 REC 37 REC 2e REC 35 REC 36 REC 37 REC 2e 1.22 1.44 1.12 1.83 1.13 1.38 1.09 1.00 REC 34 REC 18 REC 19 REC 8 REC 21 REC 34 REGIS REC 19 REC 8 REC 21

.96 .92 .95 1.35 1.26 .92 .94 .99 1.38 1.23 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

.84 .81 .82 .83 .75 .89 .81 .84 .86 .89 .79 .88 REC 32 REC 16 REC 6 REC 1 REC 3 RECle REC 23 REC 32 REC 16 REC 6 REC 1 REC 3 REcle REC 23 1.18 .97 .86 .75 .85 1.12 .88 1.09 .99 .91 .Se .91 1.16 .85 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 REC 31 REC 15 REC 5 REG 4 REC 11 REG 24

.97 1.14 1.15 1.28 .97 1.02 .94 1.18 1.22 1.36 1.02 1.00 REC 3e REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REGI3 REC 12 REC 25

.9s .97 .69 1.01 1.35 .88 1.00 .72 1.05 1.31 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26 as .79 1.13 .92 .92 .75 1.88 .9s .88 K= 1.8697 Km 1.0683 REGIONS AVC. % DIF. ONE SICMA X DIFFERENCE 1 - 19 4.68 1.76 REC 35 REC 36 REC 37 REC 2e

-7 -4 -2 -3 28 - 37 -3.57 1.66 REC 34 REC 18 REC 19 REC 8 REC 21 1 - 37 .63 4.47 -4 2 4 2 -2 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

-4 3 5 7 5 -1 REC 32 REC 16 REC 6 REC 1 REC 3 RECle REC 23 *

-7 2 6 7 7 4 -3 REC 31 REGIS REC 5 REC 4 REC 11 REC 24

-3 3 6 6 6 -1 REC 3s REC 14 REC 13 REC 12 REC 25

-2 3 5 4 -3 jl REC 29 REC 28 REC 27 REC 26 *

-5 -5 -3 -4 I$

DELTA Km .0014 &o

RPF COWPARISDN FOR 3D CALCULATIONS, FSV CYCLE 3

28. GA DIF3D, 3/27 CYC.3/247.5 EFPD, 4-CRPS, AS-BUILT REF. IMP. Km 1.0626 IS COMPARED TO THE REFERENCE CALCULATION :

15. GA CATT, 3/27 CYC.3/247.6 EFPD, 4-GRPS, AS-BUILT REF. IWP. K= 1.0838

15. GA GATT, 3/27 C 28. CA DIF3D, 3/27 C REC 35 REC 36 REC 37 REG 2s REC 35 REC 36 REC 37 REC 2s 1.28 1.42 1.18 1.01 1.16 1.31 1.e4 .95 i REC 5; REC 18 REC 19 REC 8 REG 21 REC 34 REC 18 REC 19 REC 8 REC 21

.94 .96 .93 1.34 1.25 .96 .91 .95 1.33 1.19 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 kEC17 REC 7 REC 2 REC 9 REC 22

.83 .88 .86 .83 .75 .89 .81 .83 .84 .87 .77 .86 REC 32 REGIS REC 6 REC 1 REC 3 REC 18 REC 23 REC 32 REC 16 REC 6 REC 1 kEC 3 RECle REC 23 1.18 .96 .86 .76 .86 1.13 .89 1.13 1.81 .92 .81 .91 1.15 .84 REG 31 REGIS REC 5 REC 4 REC 11 REC 24 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24

.97 1.15 1.15 1.38 .98 1.83 .97 1.22 1.25 1.39 1.03 1.00 REC 38 REC 14 REC 13 REC 17 REC 25 REG 38 REG 14 REC 13 REC 12 REC 25

.90 .97 .78 1.83 1.39 .91 1.93 .75 1.87 1.34 REC 29 REC 28 REC 27 REC 26 REC?9 REC 28 REC 27 REC 26

,, .88 1.14 .93 .94 .78 1.11 .92 .90 e

43 Km 1.0638 K= 1.0826 RECIONS AVC. 5 DIF. ONE SIGMA X DIFFERENCE 1 - 19 4.71 2.32 REG 35 EEC36 REC 37 REC 2e

-8 -8 -5 -5 28 - 37 -3.62 2.32 REC 34 REC 18 REC 19 REC 8 REC 21 1 - 37 .66 4.8e -4 1 3 -1 -5 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

-2 4 5 4 3 -4 REC 32 REC 16 REC 6 REC 1 REC 3 REGIS REC 23

-5 6 7 7 6 1 -6 REG 31 REC 15 REC 5 REC 4 REC 11 REC 24 e 6 9 7 5 -3 REC 3e REC 14 RECi3 REC 12 REC 25 1 6 7 4 -4 u) o REC 29 REC 28 REC 27 REC 26 $$

-2 -2 -2 -4 gg DELTA Km .8812 *Z E

RPF COMPARISDN FOR 3D CALCULATIONS, FSV CYCLE 3

29. GA DIF3D, 3/28 CYC.3/247.5 EFPD, 4-GRPS, AS-BUILT REF. IMP. Km 1.8888 IS COMPARED TO THE REFERENCE CALCULATION :

16. CA CATT, 3/28 CYC.3/247.5 EFPD, 4-GRPS, AS-BUILT REF. IMP. Km 1.8892

16. GA GATT, 3/28 C 29. CA DIF3D, 3/28 C REC 35 REG 36 REG 37 REC 28 REG 35 REG 36 REC 37 REC 28 1.14 1.48 1.88 .96 1.85 1.31 1.82 .98 i

REC 34 REGIS REC 19 REG 8 REC 21 REG 34 REGIS REC 19 REC 8 REG 21

.89 .89 1.88 1.31 1.18 .86 .98 1.82 1.38 1.11 REG 33 REG 17 REG 7 REG 2 REG 9 REG 22 REG 33 REG 17 REG 7 REG 2 REG 9 REG 22

, .88 .78 .81 .83 .73 .85 .79 .82 .85 .86 .74 .81

?

RFC32 REGIS REG 6 REG 1 REC 3 REGIS REC 23 REG 32 REG 16 REG 6 REG 1 REG 3 REGIS REC 23 1.16 .97 .88 .76 .87 1.14 .87 1.12 1.83 .95 .81 .91 1.14 .81 REG 31 REGIS REG S REG 4 REG 11 REG 24 REG 31 REGIS REG S REG 4 REC 11 REG 24

.99 1.28 1.18 1.33 1.88 1.85 1.08 1.37 1.28 1.41 1.12 1.81

! REC 38 REC 14 REG 13 REG 12 REG 25 REC 38 REG 14 REGI3 REG 12 REG 25

.93 .99 .69 1.84 1.42 .95 1.85 .74 1.68 1.35 REC 29 REC 28 REG 27 REG 26 REC 29 REG 28 REC 27 REC 26 co .79 1.18 .98 .92 .78 1.88 .88 .88 e

E5 K= 1.8892 K= 1.8888 REGIONS AVG. 5 DIF. ONE SIGRA X DIFFERENCE 1 1 - 19 4.39 2.71 REC 35 REC 36 REG 37 REG 28

-8 -6 -5 -6 28 - 37 -3.62 2.72 REG 34 REG 18 REG 19 REG 8 REG 21 1 - 37 .58 4.86 -4 1 2 -1 -6 REG 33 REC 17 REG 7 REG 2 REG 9 REC 22

-1 5 4 4 2 -5 REG 32 REGIS REG 6 REC 1 REG 3 REGIS REG 23

-3 6 7 7 5 8 -7 REC 31 REGIS REG S REG 4 REG 11 REG 24 2 7 8 6 4 -3 REG 38 REG 14 REC 13 REC 12 REG 25 2 6 7 3 -5 I

REC 29 REC 28 REC 27 REG 26 E$

i -2 -2 -2 -4 8; DELTA K= .8812 d

O

T ' .

RPF COMPARISDN FOR 3D CALCULATIONS, FSV CYCLE 3

36. CA DIF30, 3/29 CYC.3/268.2 EFPD, 4-CRPS, AS-BUILT REF. IWP. Km 1.0046 IS COMPARED TO TEE REFERENCE CALCULATION .

17. CA CATT, 3/29 CYC.3/268.2 EFPD, 4-GRPS, AS-BUILT REF. IMP. Km 1.0059

17. CA CATT, 3/29 C 38. CA DIF3D, 3/29 C REC 36 REC 36 REC 37 REC 2e REC 35 REC 36 REC 37 REC 2e l 1.16 1.42 1.e9 .97 1.10 1.39 1.08 .96 t REC 34 REC 18 REC 19 REC 8 REC 21 REC 34 REC 18 REC 19 REC 8 REC'el i

.99 .98 1.00 1.33 1.19 .88 .93 1.06 1.37 1.17 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REG 22

.81 .79 .81 .83 .73 .86 .79 .82 .85 .88 .77 .84 REC 32 REG 16 REC 6 REC 1 REC 3 RECle REC 23 REC 32 REC 16 REC 6 REG 1 REC 3 RECle REC 23 1.17 .98 .88 .76 .87 1.12 .85 1.09 1.00 .92 .81 .91 1.16 .82 l REC 31 REC 15 REG S REG 4 REC 11 REC 24 REC 31 REGIS REC 6 REG 4 REC 11 REC 24

.99 1.28 1.18 1.32 1.06 1.03 .96 1.31 1.24 1.32 1.18 1.00 REC 3e REC 14 REGIS REC 12 REG 25 REC 3e REC 14 REC 13 REC 12 REG 25

.92 .98 .69 1.83 1.48 .96 1.88 .72 1.96 1.33 REC 29 REG 2G REC 27 REC 26 REC 29 REC 28 REC 27 REC 26 e, .78 1.89 .89 .91 .74 1.e4 .86 .86 e

(( Km 1.0059 Km 1.6846 REGIONS AVG. 5 DIF. DNE SICMA 5 DIFFERENCE 1 - 19 4.88 1.43 REC 35 REC 36 REG 37 REC 2e

-6 -2 -1 -1 28 - 37 -3.16 1.69 REC 34 REGIS REG 19 REG 8 REC 21 1 - 37 .66 3.98 -2 4 6 3 -1 REC 33 REG 17 REG 7 REC 2 REC 9 REC 22

-3 4 5 6 6 -1 REC 32 REC 16 REC 6 REC 1 REC 3 RECle REC 23

-7 2 5 6 6 2 -4 REC 31 REC 15 REC 6 REG 4 REC 11 REC 24

-3 3 6 6 3 -3 REC 3e REC 14 REC 13 REC 12 REC 26

-2 3 4 2 -6 u) o REC 29 REC 28 REC 27 REC 26 l$

-5 -6 -4 -5 g; DELTA K= .0013 2:

O

RPF COMPARISON FOR 3D CALCULATZONS, FSV CYCLE 3

31. CA DIF30, 3/38 CYC.3/282.7 EFPD, 4-CRPS, AS-BUILT REF. IMP. Km 1.0025 IS COMPARED TO THE REFERENCE CALCULATION :

18. CA CATT, 3/38 CYC.3/282.7 EFPD, 4-GRPS, AS-BUILT REF. IMP. Km 1.0037

18. CA CATT, 3/38 C 31. CA DIF3D, 3/36 C REC 35 PEG 36 REG 37 REC 2e REC 35 REC 36 REC 37 REC 2e 1.16 1.42 1.88 .97 1.88 1.36 1.95 .93 REC 34 REC 18 REC 19 REC 8 REC 21 REC 34 REC 18 REC 19 REC 8 REC 21

.98 .98 1.08 1.33 1.19 .87 .91 1.82 1.34 1.14 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REG 33 REC 17 REC 7 REC 2 REC 9 REC 22

.81 .79 .81 .83 .73 .85 .79 .82 .84 .87 .76 .83 REC 32 REC 16 REC 6 REC 1 REC 3 RECle REC 23 REC 32 REGI6 REC 6 REC 1 REC 3 REcle REC 23 1.17 .98 .88 .77 .87 1.12 .85 1.11 1.81 .93 .81 .91 1.14 .81 REC 31 REGIS REC 5 REC 4 REC 11 REC 24 REC 31 REC 15 REC 5 REC 4 REC 11 RECT 4

.99 1.28 1.18 1.33 1.06 1.83 .98 1.34 1.25 1.48 1.18 1.be REC 3s REC 14 REC 13 REC 12 NEC25 REC 3e REC 14 REC 13 REC 12 REC 25

.92 .98 .69 1.03 1.48 .92 1.93 .74 1.26 1.35 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 kEC26 as .78 1.99 .89 .91 .76 1.87 .87 .88 I

[' Km 1.0037 Km 1.0025 REGIONS AVG. 5 DIF. ONE SIGMA  % DIFFERENCE 1 - 19 4.82 1.68 REC 35 REC 36 REC 37 REC 2e

-7 -5 -3 -4 20 - 37 -3.13 1.61 REC 34 REC 18 REC 19 REC 8 REC 21 1 - 37 .54 3.97 -3 2 2 0 -4 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

-2 4 4 5 4 -3 REC 32 REGIS REC 6 REC 1 REC 3 REcle REC 23

-5 3 6 5 5 1 -5 REC 11 REC 15 REG 5 REG 4 REC 11 REC 24

-1 5 6 5 4 -3 REC 38 REC 14 REC 13 REC 12 REG 25 e 5 7 3 -4 'o REC 29 RECJ8 REC 27 RFC26 b-

-2 -2 -2 -4 {y DELTA K= .8812 sc 5

RPF C0hPARISDN FOR 3D CALCULATIONSo FSV CYCLE 3

32. CA DIF3D, 3/31 CYC.3/282.7 EFPD, 4-CRPS, AS-BUILT REF. IWP. Km 1.se2e IS COMPARED TO THE REFERENCE CALCLA.ATION :

19. CA CATT, 3/31 CYC.3/282.7 EFPD, 4-GRPS, AS-BUILT REF. IWP. Km 1.0037

19. GA GATT, 3/31 C 32 CA DIF30. 3/31 C REC 35 RECTS REC 37 REC 2e REC 35 REC 8 REC 37 REC 2e 1.18 1.47 1.98 .97 1.88 1.34 1.e4 .94 l REC 34 REC 18 REC.4 REC 8 REC 21 REC 34 REGI8 REC 19 REG S REC 21 I

.9e .90 1.01 1.33 1.19 .87 .91 1.92 1.36 1.16 i L REC 33 REC 17 REC 7 REG '2 REG 9 REC 22 REC 33 REC 17 REC 7 REG 2 REC 9 REC 22 l .81 .79 .81 .83 .73 .85 .79* .82 .84 .87 .77 .84 REC 32 REC 16 REG S REG 1 REG S RECle REC 23 REC 32 REC 16 REG 6 REC 1 REC 3 RECle REC 23 1.16 .98 .88 .77 .87 1.12 .86 1.18 1.es .92 .81 .91 1.16 .83 REC 31 REGIS REG 5 REG 4 REGit REC 24 REC 31 REGIS REC 6 REC 4 REC 11 REC 24

.99 1.28 1.18 1.33 1.ec 1.92 .98 1.33 1.26 1.40 1.18 1.81 REC 3e REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 AEGI3 REC 12 REC 26

.92 .98 .69 1.83 1.40 .92 1.92 .73 1.06 1.36 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26 m .78 1.99 .89 .91 .77 1.87 .88 .89 s

[] Km 1.8037 Km 1.8020 RECIONS AVG. X DIF. ONE SICMA X DIFFERENCE 1 - 19 3.79 1.68 REC 35 REC 36 REC 37 REC 2e

-7 -6 -4 -4

%9 - 37 -2.76 1.74 REC 34 REC 18 REC 19 REG 8 REC 21 1 - 37 .Se 3.72 -4 1 1 1 -3 REC 33 REC 17 REG 7 REG 2 REC 9 REC 22

-2 3 4 5 5 -2 REG 32 REC 16 REG 6 REC 1 REG 3 REC 1s REC 23

-5 2 6 6 6 3 -2 REC 31 REGIS REC 6 REG 4 REC 11 REC 24

-1 4 6 5 4 -1 REC 3s REC 14 REC 13 REC 12 REC 26 e 4 7 3 -3 e

REG 29 REC 28 REC 27 REC 26

-2 -2 -1 -3 5$.

c w

DELTA Ma .0017

• d a

RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 3

33. GA DIF3D, 3/32 CYC.3/294.5 EFPD, 4-CRPS, AS-BUILT REF. IWP. K= 1.0009 IS COMPARED TO THE REFERENCE CALCULATION :

26. GA GATT, 3/32 CYC.3/294.5 EFPD, 4-CRPS, AS-BUILT REF. IMP. K= 1.0626

28. CA CATT, 3/32 C 33. CA DIF30, 3/32 C REG 35 REC 36 REG 37 REC 2e REC 35 REC 36 REC 37 REC 2e 1.16 1.43 1.88 .97 1.89 1.36 1.06 .95 REC 34 REC 18 REC 19 REC 8 2EC21 REG 34 REGIS REC 19 REC 8 REC 21

.96 .98 1.81 1.34 1.19 .87 .92 1.83 1.36 1.17 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

.81 .70 .81 .83 .73 .85 .79 .82 .84 .87 .77 .84 REC 32 REC 16 REC 6 REC 1 REC 3 REcle REC 23 REC 32 REC 16 ndC 6 REC 1 REC I REcle REC 23 1.16 .98 .88 .77 .87 1.12 .85 1.18 1.88 .92 .81 .91 1.15 .83 REC 31 REGIS REC 5 REC 4 REC 11 REC 24 REC 31 REGIS REC 5 REG 4 REC 11 REC 24

.99 1.29 1.18 1.33 1.06 1.82 .97 1.32 1.24 1.39 1.89 1.08 REC 3s REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REGIS REC 12 ' REC 25

.92 .98 .69 1.83 1.48 .91 1.81 .73 1.85 1.35 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26 m .78 1.89 .88 .91 .76 1.06 .87 .88 s

y Km 1.0626 K= 1.0009 REGIDNS AVC. X DIF. ONE SICMA X DIFFERENCE 1 - 19 3.67 1.50 REC 35 REC 36 REG 37 REC 2e

, -6 -5 -2 -2 t

28 - 37 -2.71 1.37 REC 34 REGIS REC 19 REC 8 REC 21 1 - 37 .56 3.53 -3 2 2 2 -1 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

-2 4 4 5 6 -1 REC 32 REC 16 REC 6 REC 1 REC 3 REcle REC 23

-5 2 5 5 5 2 -3 REC 31 REGIS REC 5 REC 4 REC 11 REC 24

, -2 2 5 5 3 -1 REG 3s REC 14 REGI3 REC 12 REC 25

-1 3 6 2 -3 q3 o

REC 29 REC 28 REC 27 REC 26 u)

-3 -3 -1 -4 [$

m DELTA Km .0017 g

RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 3

9. GA CATT, 3/21 CYC.3/188.8 EFPD, 4-GRPS, AS-BUILT REF. IMP. K= 1.0856 IS COMPARED TO THE REFERENCE CALCULATION :

1. GA WEASURED 3/21 FSVCOR TP624 72583 33549, 3C AT 181.8 "DUT, K= 1.0008

1. GA WEASURED 3/21 9. CA CATT, 3/21 C REC 35 REC 36 REG 37 REC 28 REG 35 REC 36 REC 37 REC 2e 1.29 1.47 1.10 .87 1.36 1.68 1.28 .94 REC 34 REC 18 REC 19 REC 8 REC 21 REC 34 REC 18 REC 19 REC 8 REG 21

.83 .83 .98 1.39 .G9 .96 .98 .87 1.27 .71 REC 33 REC 17 REG 7 REG 2 REC 9 REC 22 REC 33 REC 17 REG 7 REC 2 REG 9 REC 22

.45 .88 .97 1.03 .73 .59 .55 .82 .93 .94 .69 .77 REC 32 REC 16 REC 6 REC 1 REC 3 RECle REG 23 REC 32 REC 16 REG e REC 1 REC 3 RECle REC 23 1.18 1.12 1.09 .99 1.85 1.88 .77 1.16 .99 1.81 .93 .96 1.e4 .92 REC 31 REC 15 REG 5 REG 4 REC 11 REG 24 REG 31 REC 15 REG 5 REG 4 REC 11 REC 24

.98 1.06 1.41 1.62 .94 1.11 1.86 1.85 1.33 1.48 .98 1.13 REC 3C REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REC 13 REC 12 REC 25

.98 .95 .85 1.27 1.47 .97 .93 .78 1.06 1.51 REC 29 REG 28 REC 27 REC 26 REC 29 REC 28 REG 27 REC 26 es .83 .99 .52 .95 .84 1.85 .68 .93 e

C Km 1.0000 K= 1.0056 RECIONS AVC. X DIF. DNE SIGMA X DIFFERENCE 1 - 19 -5.99 6.17 REC 35 REC 36 REC 37 REC 2s 6 9 9 8 28 - 37 9.98 8.95 REC 34 REC 18 REC 19 REC 8 PEC21 1 - 37 1.78 11.86 15 9 -3 -9 21 REC 33 REC 17 REG 7 REG 2 REC 9 REC 22 22 -7 -4 -9 -5 38 REC 32 REC 16 REC 6 REG 1 REG 3 REC 18 REC 23

-2 -11 -8 -6 -8 4 28 REG 31 REC 15 PEG 5 REG 4 REC 11 REC 24 8 e 6 -9 -4 2 REC 38 REG 14 REC 13 REC 12 REC 25 8 -3 -18 -16 2 g>

o REC 29 REC 28 REC 27 REC 26 j&

2 6 17 -2 un m

DELTA K= .0056 z 5

RPF COMPARISON FOR 3D CALCULATION0 3 FSV CYCLE 3

11. CA GATT, 3/23 CYC.3/2es.e EFPD, 4-CRPS, AS-BUILT REF. IMP. Km 1.Sede j IS COMPARED TO THE REFERENCE CALCULATION : l

2. CA WEASURED 3/23 FSVCOR TPS26 81883 111428, 4B AT 133.8 "OUT, Km 1.9006 1

2. CA WEASURED 3/23 11. CA CATT, 3/23 C l

REC 35 REC 36 REC 37 REC 2e REC 35 REG 36 REC 37 REC 2e 1.28 1.43 1.06 .94 1.31 1.47 1.12 1.06 REC 34 REGIS REC 19 REC 8 REC 21 REC 34 REC 18 REC 19 REC 8 REC 21

.88 .97 .88 1.37 1.02 1.81 .95 .81 1.33 1.24 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

.69 .83 .87 .92 .76 .88 .88 .82 .82 .84 .77 .95 REC 32 REC 16 REC 6 REC 1 REC 3 RECle REC 23 REC 32 REC 16 REC 6 REC 1 REC 3 RECle REC 23 1.13 1.08 .93 .84 .95 1.27 .87 1.17 .94 .85 .76 .86 1.17 .95 l

REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24

.98 .95 1.27 1.49 .88 1.08 .94 .95 1.16 1.28 .83 1.85 REC 38 REC 14 REGI3 REC 12 REC 25 REC 3e REC 14 REG 13 REC 12 REC 25

.87 1.09 .78 1.13 1.35 .89 .99 .71 1.82 1.38 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26

, .83 1.13 .85 .93 .84 1.28 .92 .96 C

Km 1. sees Km 1.0648 REGIONS AVC. X DIF. DNE SIGWA X DIFFERENCE 1 - 19 -5.75 3.99 REC 35 REC 36 REC 37 REC 2s 9 3 5 13 28 - 37 7.64 6.67 REC 34 REGIS REC 19 REC 8 REC 21 1 - 37 .77 8.66 14 -2 1 -3 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 16 -1 -5 -8 2 19 REC 32 REC 16 REC 6 REC 1 REC 3 REcle REC 23 4 -6 -9 -9 -le -8 9 REC 31 REC 15 REC 6 REC 4 REC 11 REC 24 6 8 -8 -9 -6 -3 REC 38 REC 14 REC 13 REC 12 REC 2E 2 -9 -9 -le 3 e

REC 29 REC 28 REC 27 REC 26 $$

1 6 8 3 e u

DELTA Km .0048 z

b

p RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 3

13. CA CATT, 3/25 CYC.3/221.s EFPD, 4-CRPS, AS-BUILT REF. IMP. Km 1.0099 IS COMPARED TO THE REFERENCE CALCULATION :

3. GA MEASURED 3/25 FS*.*COR TP634 92983 874434, 3D AT 71.5 "OUT, Km 1. Sees

3. CA MEASURED 3/25 13. GA CATT, 3/25 C REC 35 REC 36 REC 37 REC 2e REC 36 REC 36 REC 37 REC 2e 1.19 1.31 1.01 .96 1.22 1.45 1.12 1.03 REC 34 REC 18 REC 19 REC 8 REC 21 REC 34 REGIS REC 19 REC 8 REC 21

.87 .93 .83 1.4s 1.15 .95 .92 .95 1.34, 1.27 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

.78 .82 .85 .9e .78 .79 .83 .81 .82 .84 .75 .89 REC 32 REC 16 REC 6 REC 1 REC 3 RECle REC 23 REC 32 REGIS REC 6 REC 1 REC 3 RECle REC 23 1.12 1.s1 .91 .81 .93 1.24 .81 1.16 .97 .87 .76 .85 1.12 .86 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24

.9e 1.s7 1.21 1.37 .98 .99 .96 1.14 1.15 1.28 .c7 1.01 REC 3e REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REC 13 REC 12 REC 25

.86 1.98 .77 1.13 1.32 .95 .97 .69 1.02 1.35 REG 29 REC 28 REC 27 REC 26 REC 29 REC 26 REC 27 REC 26

.88 1.12 .95 .92 .79 1.12 .92 .93 to Km 1. sees Km 1.9999 I

I [3 j RECIONS AVC. N DIF. ONE SICMA N DIFFERENCE 1 - 19 -4.44 4.83 REC 35 REC 36 R2C37 REC 2e 4

2 11 le 7 l 2e - 37 5.21 4.66 REC 34 REC 18 REC 19 REC 8 REC 21 i 1 - 37 .25 6.77 9 -1 7 -5 11 REG 33 REC 17 REC 7 REC 2 REC 9 REC 22 l 6 -2 -4 -7 -4 12

, j REC 32 REC 16 REC 6 REC 1 REC 3 REGle kEC23

] 4 -4 -5 -7 -9 -le 9 1

REC 31 REC 15 REC 5 REC 4 WEG11 REC 24 7 8 -5 -7 -1 2 REC 3e REC 14 REC 13 REC 12 REC 26 4 -le -le -le 2 .

REC 29 REC 28 REC 27 REC 26

-2 e -4 1 yj e

DELTA Km .0099 *-

t Os i O

t RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 3

15. CA CATT, 3/27 CYC.3/247.5 EFPD, 4-CRPS, AS-BUILT REF. IWP. Km 1.8038 IS COWPARED TO THE REFERENCE CALCULATION :

4. CA WEASURED 3/27 FSVCOR TP638 182983 084955, 3D AT 96.8 "OUT, Km 1. sees 4 CA WEASURED 3/27 15. CA CATT, 3/27 C REC 35 REC 36 REC 37 REC 28 REC 35 REC 36 REC 37 REC 2s 1.19 1.34 1.51 .91 1.29 1.42 1.18 1.81 REC 34 REC 18 REC 19 REC 8 REC 21 REC 34 REC 18 REC 19 REC 8 REC 21

.88 .91 .94 1.39 1.89 .94 .96 .93 1.34 1.25 EEC33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REG 9 REC 22

.77 .82 .85 .98 .76 .76 .83 .Se .Se .83 .75 .89 REC 32 REC 16 REC 6 REC 1 REC 3 RECle REC 23 REC 32 REC 16 REC 6 REC 1 REC 3 REGIS REC 23 1.13 1.e4 .93 .88 .93 1.28 .75 1.18 .96 .86 .76 .86 1.1. R9 REC 31 REC 15 REG S REC 4 REC 11 REC 24 REC 31 REGIS REC 5 REC 4 REC 11 REC 24

.93 1.19 1.22 1.38 1.85 .99 .97 1.15 1.15 1.38 .98 1.83 REC 3s REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REC 13 LEC12 REC 25

.87 1.e9 .78 1.14 1.38 .96 .97 .78 1.83 1.39 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26

.81 1.89 .91 .85 .Se 1.14 .SJ .94

[ Km 1.9006 Km 1.0038 co RECIDNS AVC. N DIF. ONE SICWA X DIFFERENCE

, 1 - 19 -5.81 2.86 REC 35 REC 38 REC 37 REC 28 i 1 3 9 12 25 - 37 7.39 5.38 REC 34 REGIS REC 19 REC 8 REC 21 1 - 37 .61 7.91 6 -1 -1 -4 15 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 8 -3 -6 -8 -1 17 REC 32 REC 16 REC 6 REG 1 REG 3 RfCle REC 23

) 7 -7 -8 -5 -7 -6 18 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 4 -3 -6 -6 -7 4 REC 3e REC 14 REC 13 REC 12 REC 25 3 -11 -le -9 7 REC 29 REC 28 REC 27 REC 26 y$

-1 4 2 11 u)

DELTA Km .0638 $

Eo 1

RPF COMPARISON FOR 30 CALCULATIONS, FSV CYCLE 3

17. CA CATT, 3/29 CYC.3/268.2 EFPD, 4-CRPS, AS-8UILT REF. IMP. Km 1.0859 IS COMPARED TO THE REFERENCE CALCULATION :

5. CA MEASURED 3/29 FSVCOR TP646 128783 e6e128, 30 AT 1e1.2 "OUT,K= 1. sees

5. CA MEASURED 3/29 17. GA CATT, 3/29 C REC 35 REC 36 REC 37 REC 2e REC 35 REC 36 REC 37 REC's 1.18 1.31 .99 .91 1.16 1.42 1.89 .97 REC 34 REGIS REC 19 REC 8 REC 21 REC 34 REC 18 REC 19 REC 8 REC 21

.89 .93 .97 1.38 1.06 .98 .98 1.80 1.33 1.19 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

.76 .82 .87 .92 .76 .74 .81 .79 .81 .83 .73 .85 REC 32 REC 16 REC 6 REC 1 REC 3 REcle REC 23 REC 32 REC 16 REC 6 REC 1 REC 3 REcle REC 23 1.89 1.e4 .95 .84 .95 1.28 .75 1.17 .96 .88 .76 .87 1.12 .85 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 REC 31 REGIS REC 5 REC 4 REC 11 REC 24

.91 1.22 1.24 1.37 1.06 .97 .99 1.28 1.18 1.32 1.06 1.83 REC 3e REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REG 13 REC 12 REC 25

.87 1.99 .78 1.12 1.32 .92 .98 .69 1.83 1.48 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26 08 .79 1.88 .98 .86 .78 1.09 .89 .91 5 Km 1. Sees Km 1.0059 RECIONS AVC. 5 DIF. ONE SICMA 5 DIFFERENCE 1 - 19 -5.14 4.35 REC 35 REC 36 REC 37 ?EC2e

-1 8 le 7 2e - 37 6.18 4.98 REC 34 REGIS REC 19 REC 8 REC 21 1 - 37 .33 7.32 1 -4 3 -3 12 REC 33 REC 17 REC 7 REG 2 REC 9 REC 22 7 -4 -7 -9 -3 15 REC 32 REC 16 REC 6 REG 1 REC 3 RECle REC 23 7 -5 -7 -9 -8 -7 13 REC 31 REC 15 REC 5 REC 4 REC 11 REeA4 9 5 -5 -4 8 6 REC 3e REC 14 REC 13 REC 12 REC 25 5 -le -12 -8 6 REC 29

-2 REC 28 1

REC 27

-1 REC 26 6

((

os DELTA Km .8659 d o

RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 3

18. CA GATT, 3/38 CYC.3/282.7 EFPD, 4-CRPS, AS-BUILT REF. IMP. Km 1.0037 IS COMPARED TO THE REFERENCE CALCULATION :

6. CA MEASURED 3/38 FSVCOR TP65e 122883 e22428, 3D AT 118.4 "OUT,K= 1.800s

6. CA MEASURED 3/38 18. CA CATT, 3/38 C REC 35 REC 36 REC 37 RE929 REC 35 REC 36 REG 37 REC 2e 1.22 1.31 .99 1.01 1.16 1.42 1.88 .97 REC 34 REC 18 REG 19 REC 8 REC 21 REC 34 REGIS REC 19 REC 8 REC 21

.84 .93 1.06 1.35 .98 .98 .96 1.ec 1.33 1.19 REC 33 'cC17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REG 2 REC 9 REC 22

.75 .83 .88 .93 .75 .71 .81 .79 .81 .83 .73 .85 REC 32 REC 16 REC 6 REC 1 REC 3 REC 18 RE C'23 REC 32 REC 16 REC 6 REC 1 REC 3 REC 1s REC 23 1.11 1.e3 .97 .88 .97 1.28 .76 1.17 .98 .88 .77 .87 1.12 .85 REC 31 REGIS REC 5 REC 4 REC 11 REC 24 REC 31 REGIS REC 5 REC 4 REC 11 REC 24

.88 1.27 1.25 1.39 1.s9 .94 .99 1.28 1.18 1.33 1.06 1.e3 REC 3e REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REC 13 REC 12 REC 25

.88 1.18 .79 1.12 1.28 .92 .98 .69 1.83 1.48 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26

, .82 1.e5 .87 .82 .78 1.89 .99 .91

x. 1.9006 K- 1.0637 RECIONS AVC. X DIF. ONE SICMA X DIFFERENCE 1 - 19 -6.14 4.07 REC 35 REC 36 REC 37 REC 2s

-5 9 9 -4 2e - 37 7.31 7.24 REC 34 REC 18 REC 19 REC 8 REC 21 1 - 37 4s 8.91 7 -3 e -1 22 REC 33 REC 17 REC 7 REG 2 REC 9 REC 22 8 -5 -8 -11 -3 19 REC 32 REGIS REC 6 REC 1 REC 3 REC 1s REC 23 5 -5 -9 -12 -le -6 13 REC 31 REGIS REC 5 REC 4 REC 11 REC 24 12 1 -6 -5 -3 18 REC 38 REC 14 REC 13 REC 12 REC 25 5 -11 -13 -8 le q3 o

REC 29 REC 28 REC 27 REG 26 u)

-5 4 2 le [;

o DELTA Km .6637 2 E

RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 3

28. CA CATT. 3/32 CYC.3/294.5 EFPD, 4-CRPS,.AS-BUILT REF. IMP. Km 1.0026 IS COMPARED TO THE REFERENCE CALCULATION :

7. GA MEASURED 3/32 FSVCOR TP652 811784 981858, 3D AT 125.6 "OUT,K= 1. Sees

7. CA WEASURED 3/32 28. GA CATT, 3/32 C REG 35 REC 36 REC 37 REC 2e REC 35 REC 36 REC 37 REC 2e 1.19 1.41 1.e4 .98 1.16 1.43 1.98 .97 REC 34 REGIS REGIS REC 8 REC 21 REC 34 REC 18 REC 19 REC 8 REC 21

.85 .92 1.83 1.34 .95 .9e .98 1.81 1.34 1.19 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 4 .74 .82 .87 .91 .74 .7e .81 .79 .81 .83 .73 .85 REC 32 REC 16 REC 6 REC 1 REC 3 RECIM REC 23 REC 32 REC 16 REC 6 REC 1 REC 3 REGIS REC 23 i

1.17 1.e4 .95 .84 .95 1.18 .75 1.16 .98 .88 .77 .87 1.12 .85 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 REC 31 REC 15 REC 6 REC 4 REC 11 REC 24

! .88 1.33 1.24 1.37 1.12 .93 .99 1.29 1.18 1.33 1.06 1.82 REG 3e REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REC 13 REC 12 REC 25

.89 1.89 .78 1.11 1.38 .92 ,98 .69 1.83 1.48 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26 os 8

.79 1.83 .86 .81 .78 1.89 .88 .91 1

4 5 Km 1. sees Km 1.0026 REGIONS AVC. X DIF. CNE SICMA X DIFFERENCE 1 - 19 -5.52 3.21 REC 35 REC 36 REC 37 REC 2e

-3 2 4 -1 28 - 37 7.08 7.59 REC 34 REC 18 REC 19 REC 8 REC 21 1 - 37 .61 8.55 6 -2 -2 e 25 REC 33 REC 17 REC 7 REC 2 REG 9 REC 22 9 -4 -6 -9 -1 21 REC 32 REC 16 REC 6 REC 1 REC 3 REcle REC 23

-1 -6 -8 -8 -8 -5 13 REC 31 REGIS REC 5 REC 4 REC 11 REC 24 12 -3 -5 -3 -6 9 REC 3e REC 14 REC 13 REC 12 REC 25 4 -le -12 -7 8 us O

! REC 29

-1 REC 28 6

REC 27 3

REC 26 12 Lg DELTA Km .se26 z

RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 3

22. CA DIF3D, 3/21 CYC.3/188.8 EFPD, 4-CRPS, AS-BUILT REF. IMP. K= 1.8656 IS COMPARED TO THE REFERENCE CALCULACON :

1. CA WEASURED 3/21 FSVCOR TP624 72583 33549, 3C AT 1e1.8 "OUT, K= 1. sees

1. CA MEASURED 3/21 22. GA DIF30, 3/21 C REC 35 REC 36 REC 37 REC 28 REC 35 REC 36 REC 37 REC 2e 1.29 1.47 1.le .87 1.22 1.45 1.14 .89 REC 34 REC 18 REC 19 REC s REC 21 REC 34 REC 18 REC 19 REC 8 . REC 21

.83 .83 .98 1.39 .59 .91 .90 .96 1.31 .71 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REG 7 REC 2 REC 9 REC 22 45 .88 .97 1.83 .73 .59 .55 .87 .99 1.00 .75 .76 REC 32 REC 16 REC 6 REC 1 REC 3 REGIS REC 23 REC 32 REGI6 REC S REC 1 REC 3 RECIS REC 23 1.18 1.12 1.99 .99 1.85 1.98 .77 1.88 1.83 1.08 .99 1.92 1.07 .88 REC 31 REC 15 REC 6 REC 4 REC 11 REC 24 REG 31 REC 15 REC 5 REC 4 REC 11 REC 24

.98 1.e5 1.41 1.62 .94 1.11 1.e2 1.18 1.42 1.57 .95 1.e8 REC 3e REC 14 REC 13 REC 12 REC 25 REC 3s REC 14 REC 13 REC 12 REC?S 9 .98 .95 .85 1.27 1.47 .95 .97 .76 1.11 1.43 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26 m .83 .99 .52 .95 .8s 1.02 .Se .88 i

y Km 1.80 0 Km 1.8656 i

RECIDNS AVC. X DIF. DNE SIGMA X DIFFERENCE

~

1 - 19 -1.11 5.54 REC 35 REC 36 REC 37 REC 29

-5 -1 3 2 28 - 37 5.58 18.91 REC 34 REC 18 REC 19 REC 8 REC 21 1 - 37 2.11 9.le 9 9 8 -6 21 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 23 -2 2 -3 2 28 REC 32 REC 16 REC 6 REC 1 REC 3 RECle REC 23

-8 -7 -1 8 -2 7 14 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 4 3 8 -3 1 -2 REC 3e REC 14 REC 13 REC 12 REC 25 5 1 -12 -13 -3 q3 o

REC 29 REC 28 REC 27 REC 26 u)

-3 3 17 -7 [l o%

DELTA Km .6666 =g

! 25

v .. - , . .

RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 3 4

24. CA DIF30, 3/23 CYC.3/20s.e EFPD, 4-CRPS, AS-BUILT REF. IMP. Km 1.se26 -

IS COedPARED TO THE REFERENCE CALCULATION :

2. CA MEASURED 3/23 FSVCOR TP626 81883 111428, 48 AT 133.8 "OUT, K= 1.Sese

2. CA MEASURED 3/23 24. CA DIF30, 3/23 C t

REC 35 REG 36 REC 37 REC 2e REC 36 REC 36 REC 37 REC 2e 1.28 1.43 1.06 .94 1.18 1.34 1.e4 .97 REC 34 REC 18 EEC19 REC 8 REC 21 REC 34 REGIS REC 19 REC 8 REC 21

.88 .97 .Se 1.37 1.82 .96 .94 .82 1.31 1.16 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

.69 .83 .87 .92 .76 .88 .Se .87 .87 .88 .79 .98 PEC32 REC 16 REC 6 REC 1 REC 3 REcle REC 23 REC 32 REC 16 REO 6 REC 1 REC 3 RECle REC 23 1.13 1.se .93 .84 .95 1.27 .87 1.13 1.se .94 .83 .92 1.17 .89 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 REG 31 REC 15 REC 5 REC 4 REC 11 REC 24

.90 .95 1.27 1.48 .88 1.s8 .95 1.02 1.27 1.38 .88 1.81 REC 3s REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REC 13 REC 12 REC 25

.87 1.e9 .78 1.13 1.35 .98 1.e5 .77 1.07 1.32 REC 29 REC 28 REC 27 RZC26 REC 29 REC 28 REC 27 REC 26 .

.83 1.13 .85 .93 .83 1.18 .02 .93 y Km 1.000s Km 1.0626 RECIONS AVC. X DIF. ONE SIGMA X DIFFERENCE 1 - 19 .71 3.71 REC 35 REC 36 REC 37 REC:e

-2 -7 -2 4 2e - 37 3.19 6.53 REC 34 REGIS REC 19 REC 8 REC 21 1 - 37 1.19 5.56 9 -2 3 -4 14 REC 33 REG 17 REC 7 REC 2 REC 9 REC 22 16 5 e -4 4 12 REG 32 REC 16 REC 6 REC 1 REC 3 REcle REC 23 e e 1 -1 -4 -8 2 REC 31 REC 15 REC 5 REG 4 RFC11 NEC24 5 8 e -1 -1 -6 REC 3e REC 14 REGIS REC 12 REC 25 4 -4 -2 -5 -2 '

o REC 29 8

REC 28 4

REC 27 8

REC 26

-1 8o w

DELTA Km .8826 do

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

o -

RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 3 ,

26. CA DIF3D, 3/25 CYC.3/221.s EFPD, 4-CRPS, AS-BUILT REF. IWP. Km 1.0084 IS COMPARED TO THE REFERENCE CALCULATION

3. CA MEASURED 3/25 FSVCOR TP634 v2983 874524, 3D AT 71.5 "OUT, Km 1. sees 1

3. CA WEASURED 3/25 26. CA DIF3D, 3/25 C REC 35 REG 36 REC 37 REC 2e REC 35 REC 36 REC 37 REC 2e 1.19 1.31 1.e1 .96 1.13 1.37 1.le 1.01 REG 34 REC 18 REC 19 REC 8 REC 21 REC 34 REC 18 REC 19 REC 8 REC 21

.87 .93 .83 1.48 1.15 .91 .94 .99 1.38 1.25 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

.70 .82 .85 .9e .78 .79 .Se .83 .86 .89 .88 .89 REC 32 REC 16 REC 6 REC 1 REC 3 RECIS REC 23 REC 32 REGIS REG 6 REC 1 REC 3 RECle REC 23 1.12 1.81 .91 .81 .93 1.24 .81 1.97 .94 .91 .88 .91 1.17 .86 REC 31 REGIS REC 5 REC 4 REC 11 REC 24 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24

.98 1.87 1.21 1.37 .98 .99 .93 1.17 1.22 1.36 1.e2 1.81 REC 3e REC 14 REG 13 REC 12 REC 25 REC 3e REC 14 REC 13 REC 12 REC 25

.86 1.88 .77 1.13 1.32 .88 .99 .72 1.e5 1.31 l REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 PEC26 l es .88 1.12 .95 .92 .75 1.87 .9e .89 I

, 7 Km 1. sees Km 1.9984 1

REGIONS AVC. X DIF. ONE SICMA 5 DIFFERENCE i 1 - 19 .22 4.91 REC 35 REC 36 REG 37 REC 28

-5 S S 5 28 - 37 1.67 5.49 REC 34 REGIS REC 19 REC 8 REC 21 1 - 37 .78 E.21 5 1 11 -1 9 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 2 1 1 -1 2 12 REC 32 REC 16 REC 6 REC 1 REC 3 RECIS REC 23

-4 -3 6 -1 -2 -5 7 REC 31 REGIS REC 5 REC 4 REC 11 REC 24 3 9 1 -1 4 2 REC 3e REC 14 REC 13 REC 12 REC 25 2 -8 -6 -7 -1 gj REC 29 REC 28 REC 27 REC 26 5!

-7 ~4 -6 -3 yl DE:.TA K= .0084 2:

3 4

RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 3

29. CA DIF30, 3/27 CYC.3/247.5 EFPD, 4-CRPS, AS-BUILT REF. Ir. Km 1.9926 IS COMPARED TO THE REFERENCE CALCULATION :

4. CA MEASURED 3/27 FSYCOR TP638 192903 984955, 3D AT 98.e *0UT, K= 1. sees

4. CA MEASURED 3/27 28. CA DIF30, 3/27 C L

REC 35 REC 36 REC 37 REC 2e REC 35 REC 36 REC 37 REC 2e 1.19 1.34 1.01 .91 1.le 1.34 1.e4 .95 REC 34 REcle REC 19 REC e REC 21 REC 34 RECle REC 19 REC e REC 21

.88 .91 .9d 1.39 1.89 .90 .91 .95 1.33 1.19 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

.77 .82 .85 .9e .76 .76 .31 .83 .84 .87 .77 .96 REC 32 REGIS REC 6 REC 1 REC 3 REcle REC 23 REC 32 REGIS REC 6 REC 1 REC 3 RECle REC 23 1.10 1.e4 .93 .Se 93 1.2e .75 1.13 1.91 .92 .81 .91 1.15 .84 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24

.93 1.19 1.22 1.38 1.05 .99 .97 1.22 1.25 1.39 1.93 1.se REC 3e REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REC 13 REC 12 REC 25

.87 1.09 .78 1.14 1.3e .91 1.83 .75 1.07 1.34 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26 to .81 1.09 .91 .85 .78 1.11 .92 .98 1

U K= 1.8088 Km 1.0026 REGIONS AVC. X DIF. ONE SICMA 5 DIFFERENCE 1 - 19 -1.4e 2.69 REC 35 REC 36 REC 37 REC 2e  !

-7 e 4 6 28 - 37 3.46 4.75 REC 34 REGIS REC 19 REC S REC 21 1 - 37 .96 4.51 2 e 1 -4 9 REC?3 REC 17 REC 7 REC 2 REC 9 REC 22 6 1 -1 -4 1 13 REC 32 REf.16 REC 6 REC 1 REC 3 RECle REC 23 i 2 -3 -1 1 -2 -5 11 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 4 3 2 1 -2 1 REC 3e REC 14 REC 13 REG 12 REC 25 e 5 -6 -4 -6 2 o w

t REC 29

-3 REC 28 2

REC 27 e

REC 26 6

m ,

DELTA Km .0026 k O

I 4

- , - - . . - - ,-,.-- --- ,,-, , -- , e . .,, , . . -

RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 3

38. CA DIF3D, 3/29 CYC.3/268.2 EFPD, 4-CRPS, AS-BUILT REF. IMP. Km 1.0646 IS COMPARED TD THE REFERENCE CALCLA.ATION :

5. CA MEASURED 3/29 FSVCOR TP646 128783 e68128, 30 AT 181.2 "OUT,Km 1.066s

5. CA WEASURED 3/29 38. CA DIF30, 3/29 C REG 35 REC 36 REC 37 REC 2e REG 35 REC 36 REC 37 REC 2e 1.18 1.31 .99 .51 1.18 1.32 1.98 .96 REC 34 REC 18 REC 19 REC 8 REC 21 REC 34 REGIS REC 19 REC 8 REC 21

.89 .93 .97 1.38 1.06 .88 .93 1.05 1.37 1.17 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

.76 .82 .87 .92 .76 .74 .79 .82 .85 .38 .77 .34 REC 32 REGIS stEC 6 REC 1 REC 3 REC 18 REC 23 REC 32 REC 16 REC 6 REC 1 REC 3 REC 18 REC 23 1.89 1.e4 .95 .84 .95 1.28 .75 1.e9 1.06 .92 .31 .91 1.15 .82 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 REC 31 REC 15 REC 6 REC 4 REC 11 REC 24

.91 1.22 1.24 1.37 1.96 .97 .96 1.31 1.24 1.38 1.18 1.es REC 3e REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REGIS REC 12 REC 25

.87 1.99 .78 1.12 1.32 .9e 1.Se .72 1.05 1.33 REC 29 REC 28 REC 27 REC 26 REG 29 REC 28 REC 27 REC 26 cs e

.79 1.88 .96 .86 .74 1.e4 .86 .86

$ Km 1.886e Km 1.8846 RECIDNS AVC. X DIF. DNE SICWA X DIFFERENCE 1 - 19 -1.28 4.53 REC 35 REC 36 REC 37 REC 2e

-6 6 9 6 28 - 37 2.78 5.85 REC 34 REC 18 REC 19 REC 8 REC 21 1 - 37 .69 5.54 -1 8 8 e 11 REG 33 REC 17 REC 7 REC 2 REC 9 REC 22 4 8 -1 -4 2 13 REC 32 REC 16 REC 6 REC 1 REC 3 RECIS REC 23 0 -4 -3 -3 -4 -5 9 REC 31 REGIS REC 5 REC 4 REC 11 REC 24 5 8 8 1 3 3 REC 3e REC 14 REC 13 REC 12 REC 25 u>

3 -8 -8 -7 1 Cg REC 29 REC 28 REC 27 REC 26 $5

-6 -4 -5 1 C' 2:

DELTA Km .3846 };

~

RPF COWPARISDN FOR 3D CALCULATIONS, FSV CYCLE 3

31. CA DIF3D, 3/38 CYC.3/282.7 EFPD, 4-CRPS, AS-BUILT REF. IMP. Km 1.0825 IS COMPARED TO THE REFERENCE CALCULATION :

6. CA WEASURED 3/38 FSVCOR TP658 122803 822428, 3D AT 118.4 '0UT,K= 1.8988

6. CA WEASURED 3/38 31. CA DIF3D, 3/38 C REC 35 REC 36 REC 37 REC 28 REC 35 REC 36 REC 37 REC 28 1.22 1.31 .99 1.81 1.88 1.36 1.85 .93 REC 34 REGIS REC 19 REC 8 REC 21 REC 34 REGIS REC 19 REC S REC 21 i

.84 .93 1.98 1.35 .98 .87 .91 1.82 1.34 1.14 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

.75 .83 .88 .93 .75 .71 .79 .32 .84 .87 .76 .83 REC 32 REC 16 REC 6 REC 1 REC 3 RECIS REC 23 REC 32 REC 16 REC 6 REC 1 REC 3 RECIS REC 23 1.11 1.83 .97 .88 .97 1.25 .78 1.11 1.81 .93 .81 .91 1.14 .81 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 REC 31 REC 15 REC 5 REG 4 REC 11 REC 24

.88 1.27 1.25 1.39 1.89 .94 .98 1.34 1.25 1.48 1.18 1.88 REC 38 REC 14 REC 13 REC 12 REC 25 REC 38 REC 14 REC 13 REC 12 REC 25

.88 1.18 .79 1.12 1.28 .92 1.83 .74 1.06 1.35 REC 29 REC 2e REC 27 REC 26 REC 29 REC 2s REC 27 REC 26

, .82 1.85 .87 .32 .76 1.87 .37 .88 l

b u

K= 1.8888 Km 1.SS25 RECIONS AYC. X DIF. ONE SIGMA X DIFFERENCE 1 - 19 -2.48 3.61 REC 35 REG 36 REC 37 REC 28

-11 4 6 -8 28 - 37 3.96 7.33 REC 34 REGIS REG 19 REC 8 REC 21 1 - 37 .69 6.58 4 -1 2 -1 17 REC 33 REC 17 REC 7 REC 2 REC 3 REC 22 6 -1 -4 -6 1 16 REC 32 REC 16 REC 6 REC 1 REC 3 REGIS REC 23 8 -2 -4 -8 -6 -5 7 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 11 6 S S S 7 REC 38 REC 14 REC 13 REC 12 REC 26 6 -6 -7 -6 6 ,

o REC 29 REC 28 REC 27 REC 26 e

-7 2 8 7 DELTA Km .9825 g O

RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 3

33. CA DIF30, 3/32 CYC.3/294.5 EFPD, 4-CRPS, AS-BUILT REF. IMP. Km 1.See9 IS COMPARED TO THE REFERENCE CALCULATION

7. CA MEASURED 3/32 FSVCOR TP652 011784 se1968, 3D AT 126.6 "OUT,Km 1. Sees

7. CA MEASURED 3/32 33. CA DIF30, 3/32 C REC 35 REC 36 REC 37 REC 2e REC 35 REC 36 REC 37 REC 2e 1.19 1.41 1.e4 .98 1.99 1.36 1.06 .96 REC 34 RECIS REC 19 REC S REC 21 REC 34 REGIS REC 19 REC 8 REC 21

.36 .92 1.P3 1.34 .96 .87 .92 1.83 1.36 1.17 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

.74 .02 .87 .91 .74 .78 .79 .82 .84 .87 .77 .84 REC 32 REGIS REC 6 REC 1 REC 3 REGIS REC 23 REC 32 REC 16 REC 6 REC 1 REC 3 REGIS REC 23 1.17 1.94 .95 .84 .95 1.18 .75 1.18 1.88 .92 .81 .91 1.15 .33 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24 REC 31 REC 15 REC S REC 4 REC 11 REC 24

.88 1.33 1.24 1.37 1.12 .93 .97 1.32 1.24 1.39 1.99 1.es REC 3e REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REGIS REC 12 REC 26

.89 1.89 .78 1.11 1.38 .91 1.01 .73 1.06 1.36 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26 os .79 1.83 .86 .81 .76 1.96 .87 .84 s

'c$ Km 1. Sees Km 1.0009 ,

REGIONS AVC. 5 DIF. ONE SICMA 5 DIFFERENCE 1 - 19 -2.e7 3.e2 REC 36 REC 36 REC 37 REC 2e

-8 -3 1 -3 2e - 37 4.22 8.26 REG 34 REC 18 REC 19 REC S REC 21 1 - 37 .99 6.85 3 -1 -1 2 23 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 7 e -2 -4 S 28 REC 32 REC 16 REC 6 REC 1 REC 3 REcle REC 23

-6 -4 -4 -3 -3 -3 le REC 31 REGIS REC 5 REC 4 REC 11 REG 24 18 -1 e 2 -3 8

. REC 3e REC 14 REC 13 REC 12 REC 25 2 -7 -7 -5 4 g REC 29 REC 28 REC 27 REC 26 $

-4 2 2 8 g DELTA Km .00e9 2:

l l

909436 N/C l l

l 6

APPENDIX C THREE-DIMENSIONAL RADIAL PEAKING FACTOR COMPARISONS FOR CYCLE 4 m

e W

e e

f C-1

o .

RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 4

7. 3D NODAL DIF3D 4/4 CYC4/ 4.9 EFPD, 4-CRPS, AS-BUILT REF. IMP. Km 1.6165 IS COMPARED TO THE REFERENCE CALCULATION :

1. 3D GATT, 4/4 R 4/ 4.9 EFPD, 4-GRPS, AS-DUILT REF. IMP. K= 1.8165

1. 3D CATT, 4/4 7. 3D NODAL DIF3D 4~4 REC 35 REC 36 REC 37 REC 2e REG 35 REG 36 REC 37 REC 2e l 1.09 1.57 .95 .47 .84 1.22 .79 .43 REC 34 REC 18 REC 19 REC 8 REC 21 REC 34 REC 18 REC 19 REC 8 REG 21

.51 .97 .84 .83 .84 .46 .89 .81 .03 .88 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REG 7 REC 2 REC 9 REC 22

.83 .76 1.11 1.17 .74 .79 .79 .88 1.16 1.24 .79 .68 REG 32 REGI6 REC 6 REG 1 REC 3 REcle RECN3 REC 32 REGIS RfC 6 REC 1 REC 3 REcle REC 23

.51 .60 1.23 1.43 2.11 .84 .78 .58 .66 1.32 1.52 2.23 .96 .66 REC 31 REC 15 REu 5 REC 4 REC 11 REC 24 REC 31 REC 15 REC 5 REC 4 REC 11 REC 24

.72 1.07 1.86 2.23 1.94 1.06 .73 1.15 2.81 2.48 1.12 1.06 REC 30 REC 14 REC 13 REC 12 REC 25 REC 3e REC 14 REC 13 REC 12 REC 25

.84 .73 1.18 .80 1.38 .83 .86 1.28 .88 1.38 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26 n 1.01 .61 .66 .51 .95 .63 .69 .51

! 8 b3 Km 1.0165 Km 1.e199 REGIONS AVC. X DIF. ONE SICMA 5 DIFFERENCE

] 1 - 19 5.58 4.70 REC 35 REC 36 REC 37 REC 2e j -23 -22 -17 -9

20 - 37 -6.10 7.79 REC 34 REC 18 REC 19 REC e REC 21 1 - 37 .10 8.64 -19 -8 -4 8 -5 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

-5 5 5 6 7 ~3 REG 32 REC 16 REC 6 REC 1 REC 3 RECle REC 23

-2 le 7 6 6 7 -S REG 31 REGIS REC 5 REG 4 REC 11 REC 24 1 7 8 6 8 -6 REC 38 REC 14 REC 13 REC 12 REC 25

-1 le 8 IS -6 e O

REC 29 REC 28 REC 27 REC 26 $$

~6 3 5 0 w j os DELTA K= .0034 :z:

o i

RPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE 4

8. 3D NDDAL DIF3D 4/5 CYC4/ 8.9 EFPD, 4-GRPS, AS-BUILT REF. IWP. Km 1.0879 IS COMPARED TO THE REFERENCE CALCULATION :

2. 3D CATT, 4/5 CYC. 4/ 8.9 EFPD, 4-CRPS, AS-BUILT REF. IMP. Km 1.0039

2. 3D GATT, 4/5 C 8. 3D NODAL DIF3D 4/5 REG 35 REC 36 REC 37 REC 28 REC 35 REC 36 REC 37 REC 28 1.11 1.58 .96 .49 .95 1.36 .87 .47 REC 34 REC 18 REC 19 REC 8 REC 21 REC 34 REGIS REC 19 REC 8 REC 21

.54 .99 .84 .84 .88 .52 .96 .85 .87 .86 REG 33 REG 17 REG 7 REG 2 REG 9 REC 22 REG 33 REG 17 REG 7 REG 2 REG 9 REC 22

.89 .78 1.08 1.13 .74 .74 .87 .82 1.13 1.19 .88 .72 REG 32 REC 16 REG S REG 1 REC 3 REC 18 REG 23 REC 32 REG 16 REG 6 REG 1 REG 3 REcle REC 23

.55 .63 1.19 1.35 2.83 .84 .72 .55 .67 1.26 1.41 2.11 .89 .68 REG 31 REG 15 REG 5 REC 4 REC 11 REG 24 REC 31 REC 15 REG 5 REG 4 REC 11 REG 24

.77 1.08 1.77 2.11 1.92 1.05 .76 1.13 1.87 2.22 1.08 1.se REC 3e REC 14 REC 13 REC 12 Et:e.25 REC 3e REC 14 "EC13 REC 12 REG 25

.88 .74 1.16 .79 1.38 .85 .71 1.23 .85 1.30 REC 29 REC 28 REC 27 REC 26 REG 29 ret REC 27 REG 26 j n 1. 8 .64 .68 .52 . 9C. . .69 .52 da Km 1.0039 Km I %B 69 RECIONS AVG. % DIF. DNE SICWA  % DIFFERENCE 1 - 19 4.91 2.45 REC 35 REC 36 REC 37 REC 28

-14 -14 -9 -4 2e - 37 -4.47 4.54 REG 34 REC 18 REC 19 REC 8 REC 21 1 - 37 .35 5.94 -4 -3 1 4 -2 REC 33 REC 17 REG 7 REC 2 REC 9 REC 22 l

-2 5 5 5 8 -3 REC 32 REC 16 REG 6 REG 1 REG 3 REGls REC 23 e 6 6 4 4 6 -6 REC 31 REGIS REC 5 REC 4 REG 11 REC 24

-1 5 6 5 6 -5 REC 30 REC 14 REC 13 REC 12 REC 25

-3 7 6 8 -6 u) o REC 29 REC?8 REC 27 REC 26 $$

-8 0 1 6 La

<n I

DELTA K= .0038 m:

5

RPF CO WARISON FOR 3D CALCULATIONS, FSV CYCLE 4

9. 30 NODAL DIF3D 4/6 CYC4/ 8.9 EFPD, 4-CRPS, AS-BUIL1 REF. IMP. Km 1.e282 IS COMPARED TO THE REFEPENCE CALCULATION :

3. 3D CATT, 4/6 CYC. 4/ b.0 EFPD, 4-GRPS, AS-BUILT REF. IMP. Km 1.e212

]

3. 3D CATT, 4/6 C 9. 3D NODAL DIF3D 4/6 REC 35 REC 36 REC 37 REC 2e REC 35 REC 36 REC 37 REC 29 1.33 1.41 .89 .83 1.22 1.34 .86 .79 REGu4 REC 18 REu19 REC 3 REC 21 REC 34 REC 18 REC 19 REC 8 REC 21 1.12 1.25 .67 .79 1.26 1.85 1.26 .72 .82 1.21 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 REC 33 REC 17 REC 7 REC 2 REC 9 REC 22 1.33 .78 .77 .74 .72 1.59 1.28 .82 .84 .82 .79 1.53 4

REG 32 REC 16 REG 6 REG 1 REC 3 REcle REC 23 REC 32 REGI6 REC 6 REG 1 REC 3 REGIS REC 23 1.11 .62 .78 .79 1.36 1.66 1.06 .97 .63 .85 .88 1.44 1.13 .97 REC 31 REGIS REC 5 REC 4 REG 11 REC 24 REC 31 REC 15 REC 5 REC 4 REC 11 REG 24

.84 .87 1.14 1.22 .72 .97 .78 .91 1.26 1.37 .88 .96 REC 30 REC 14 REC 13 REC 12 REC 25 REC 3s REC 14 REC 13 REC 12 REC 25

.93 .96 1.01 .62 1.13 .89 1.06 1.66 .66 1.18 REC 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26 n 1.56 1.41 .91 .76 1.41 1.31 .87 .72 0

Km 1.0212 Km 1.8202 REGIONS AVC. X DIF. ONE SICWA X DIFFERENCE 1 - 19 7.64 3.57 REG 35 REC 36 REC 37 REC 2e

-8 -5 -3 -6 20 - 37 -5.76 3.02 REC 34 REC 18 REC 19 REC 8 REC 21 1 - 37 1.12 7.54 -6 1 7 4 -4 i

REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

-18 4 9 11 9 -4 REC 32 REC 16 REC 6 REC 1 REC 3 REGIS REC 23

-13 2 18 12 11 7 -3 REC 31 REC 15 REC 5 REG 4 REC 11 REC 24

-7 5 11 12 11 8 REC 38 REC 14 REG 13 REC 12 REC 25

-5 4 5 7 -3 go REC 29 REC 28 REC 27 REC 26 5$

-10 -7 -5 -6

((

DELTA K= .0010 sc

~

~

RPF COMPARISDN FOR 3D CALCULATIONS, FSV CYCLE 4

19. 3D NODAL DIF30 4/7 CYC4/17.4 EFPD, 4-GRPS, AS-BUILT REF. IMP. Km 1.0044 IS COMPARED TD THE REFERENCE CALCULATION :

4. 3D CATT, 4/7 CYC. 4/17.4 EFPD, 4-CRP3, AS-BUILT REF. IMP. Km 1.0006

4. 3D CATT, 4/7 C 35. 30 NODAL DIF3D 4/7 REC 35 REC 36 REC 37 REC 2s REC 35 REC 36 REC 37 REC 2s l 1.38 1.42 .89 .82 1.16 1.29 .91 .76 )

REC 34 REC 18 REC 19 REG 8 RECT 1 REC 34 REGIS REC 19 REG 8 REC 21 1.08 1.24 .61 .79 1.24 1.06 1.22 .71 .81 1.17 REGJ3 REC 17 REG 7 REG 2 REG 9 REC 22 REC 33 REG 17 REG 7 REG 2 REG 9 REC 22 1.31 .78 .78 .76 .73 1.57 1.19 .81 .85 .84 .79 1.48 REC 32 REG 16 REG 6 REC 1 REC 3 RECle REC 23 REG 32 REG 16 REG 6 REC 1 REG 3 REGIS REC 23 1.88 .61 .79 .82 1.36 1.06 .98 .98 .64 .88 .92 1.51 1.12 .94 REG 31 RE,t15 REG 5 REG 4 REG 11 REC 24 REC 31 REGIS REG S REG 4 REC 11 REC 24

.82 .87 1.17 1.28 .75 .97 .78 .94 1.36 1.45 .83 .96 REC 3s REG 14 REC 13 REG 12 REC 25 REG 3e REC 14 REC 13 REG 12 REC 25

.91 .94 1.92 .63 1.16 .88 .9C 1.09 .69 1.13 REG 29 REC 28 REC 27 REC 26 REG 29 REG 28 REC 27 REC 26 1.52 1.35 .89 .76 1.38 1.28 .87 .74 n

i La K= 1.0058 Km 1.0644 REGIONS AVC. X DIF. DNE SICMA X DIFFERENCE 3 - 19 7.74 3.91 REC 35 REC 36 REC 37 REC 2e

-11 -9 -6 -7 26 - 37 -5.90 2.98 REG 34 REC 18 REC 19 REG 8 REC 21 1 - 37 1.16 7.72 -8 -2 6 3 -6 REC 33 REC 17 REG 7 REG 2 REG ? REC 22

-9 4 9 11 3 -6 REC 32 REC 16 REG 6 REG 1 REC 3 REC 1s REC 23

-le 5 11 12 11 6 -4 REG 31 REGIS REG S REC 4 REG 11 REC 24

-4 7 12 13 11 -1 REG 38 REC 14 REC 13 REG 12 REG 25

-3 5 7 18 -2 gg REG 29 REC 23 REC 27 REG 26 5$

-9 -5 -2 -3 y*

D ,.TA K= .0006 g n

CPF COMPARISON FOR 3D CALCULATIONS, FSV CYCLE O

11. 3D NODAL DIF3D 4/8 CYC4/17.4 EFPD, 4-CRPS, AS-BUILT REF. IMP. Km 1.0856 IS COMPARED TO THE REFERENCE CALCLA.ATION :

5. 3D CATT, 4/8 CYC. 4/17.4 EFPD, 4-CRPS, AS-BUILT REF. IMP. Km 1.0061

5. 3D CATT, 4/8 C 11. 30 N00AL DIF3D 4/8 REC 31 aEG2? REC 37 REG 2a REC 35 REC 36 REC 37 REC 28 1.30 1.41 .88 .82 1.15 1.28 .83 .76 REC 34 REC 18 REC 19 REC 8 REC 21 REC 34 REC 18 REC 19 REC 8 REC 21 1.98 1.25 .68 .79 1.25 .99 1.22 .71 .81 1.17 i REC 33 REG 17 REG 7 REG 2 REC 9 REC 22 REC 33 REC 17 REG 7 REC 2 REC 9 REC 22 i

1.38 .78 .78 .76 .73 1.57 1.19 .81 .85 .84 .79 1.48 REC 32 REC 16 REC 6 REC 1 REG 3 REcle REG 23 REC 32 REC 16 REC 6 REC 1 REC 3 REC 18 REC 23 1.87 .61 .88 .82 1.37 1.06 .98 .97 .63 .88 .92 1.51 1.12 .94 REC 31 REC 15 REC 6 REC 4 REC 11 REC 24 REC 31 REC 15 REC 6 REG 4 REC 11 REC 24

.81 .87 1.17 1.29 .75 .97 .78 .94 1.31 1.45 .83 .96 REG 3e REC 14 REC 13 REC 12 REC 25 kECT* REC 14 REC 13 REC 12 REC 25

.91 .95 1.02 .63 1.16 .89 .99 1.18 .69 1.13 REC 29 REC 28 REC 27 REC 26 REG 29 REui' REC 27 REC 26 n 1.52 1.35 .89 .76 1.39 1.29 .87 .73 B

C' Km 1.0661 Km 1.0056 REGIONS AVG. 5 DIF. DNE SICMA 5 DIFFERENCE 1 - 19 7.66 3.84 REC 35 REC 36 REC 37 REC 2e f

-11 -9 -6 -7 j 20 - 37 -5.89 2.98 REC 34 REC 18 REG 19 REG 8 REC 21 1 - 37 1.07 7.66 -8 -2 4 3 -6 i

REC 33 REC 17 REC 7 REC 2 REC 9 REC 22

-9 4 9 11 8 -6 REC 32 REC 16 REC 6 REC 1 REC 3 REcle REC 23

-le 5 11 12 le 6 -4 REC 31 REC 15 REG S REC 4 REC 11 REC 24

-4 7 12 13 11 -1 REC 3e REC 14 REC 13 REC 12 REC 25 q>

-3 5 7 18 -2 c) u)

REC 29 REC 28 REC 27 REC 26 $$

-9 -5 -2 -3 C'

2:

DELTA Km .0005 --

O

- . = _

~

~ *

, . . .  ? .

RPF COMPARISON F02 3D CALCULATIONS, FSV CYCLE 4

12. 30 NDDAL DIF3D 4/9 CYC4/24.9 EFPD, 4-CRPS, AS-BUILT REF. IWP. K= 1.0649 IS COMPARED TD TifE REFERENCE CALCULATION :

6. 3D CATT, 4/9 CYC. 4/24.9 EFPD, 4-CRPS, AS-BUILT REF. IMP. Km 1.0665

6. 3D CATT, 4/9 C 12. 30 NODAL DIF3D 4/9 REC 35 REC 36 REC 37 REC 23 REC 35 REG 36 REC 37 REC 2e 1.28 1.48 .88 ,81 1.17 1.38 .84 .76 REC 34 REC 18 REC 19 REG e REC 21 REC 34 REC 18 REC 19 REC 8 REG 21 1.87 1.25 .68 .79 1.25 1.01 1.24 .72 .82 1.19 REC 33 REC 17 REG 7 REG 2 REG 9 REC 22 REC 33 REG 17 REG 7 REG 2 REC 9 REC 22 1.31 .78 .78 .76 .74 1.58 1.21 .82 .85 .84 .86 1.58 REC 32 REC 16 REG 6 REG 1 REC 3 RECle REC 23 REC 32 REC 16 REG 6 REG 1 REC 3 RECle REG 23 1.07 .61 .88 .83 1.38 1.66 .96 .98 .64 .87 .91 1.51 1.12 .94 REC 31 REC 15 REO 5 REG 4 REG 11 REG 24 REC 31 REGIS REG S REG 4 REC 11 REC 24

.81 .87 1.18 1.38 .75 .97 .78 .93 1.29 1.44 .83 .95 REC 3s REG 14 REC 13 REC 12 REG 25 REC 3e REC 14 REG 13 REC 12 REC 25

.91 .94 1.53 .S3 1.15 .88 .98 1.89 .68 1.12 REG 29 REC 28 REC 27 REC 26 REC 29 REC 28 REC 27 REC 26 1.52 1.34 .88 .75 1.38 1.27 .86 .72 Km 1.0055 Km 1.0649 REGIONS AVG. % DIF. DNE SICWA X DIFFERENCE 1 - 19 7.07 2.91 REG 35 REC 33 PEc 7 REC 2e

-9 -7 -4 -6 20 - 37 -5.32 2.17 REG 34 REGIS REC 19 REG 8 REC 21 1 - 37 1.04 6.77 -6 8 6 4 -5 REC 33 REC 17 REG 7 REG 2 REG 9 REC 22

-8 6 8 le 8 -5 REC 32 REC 16 REG 6 REG 1 REG 3 REC 18 REG 23

-9 5 9 le 9 5 -4 REG 31 REGIS REG 6 REG 4 REG 11 REC 24

-4 6 9 11 IS -2 e

REC 3s REC 14 REGI3 REC 12 REC 25 $$

-4 4 6 8 -3 s; REG 29 REG 28 REC 27 REC 26

-9 -6 -3 -4 C DELTA K= .0006

- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _