ML19327C154
| ML19327C154 | |
| Person / Time | |
|---|---|
| Site: | University of Virginia |
| Issue date: | 01/31/1989 |
| From: | Fehr M VIRGINIA, UNIV. OF, CHARLOTTESVILLE, VA |
| To: | |
| Shared Package | |
| ML19327C150 | List: |
| References | |
| NUDOCS 8911210026 | |
| Download: ML19327C154 (93) | |
Text
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i-4 Design Optimisation of a Low Barichment k University of virginia ar - Nuclear Reactor (1: -.
srfra! arm.ararastknMEw5camas- G *u ' '* NN# * '"'98 ACXHOULEDGEIII11T This vorh wac perforn?d ui.13 cuppa t f m i y, Departnent of Energy Granta
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- DEFG0500E275380 cud
- DEFG0586En75273 A Thesis Presented to f
l the Faculty of the School of Engineering and Applied Science University of Virginia I-l I
1 In Partial Fulfillment I .
of the Requirer.ents.for the Degree Master of' Science (Nuclear Engineering)
['
bY Mary Katherine Fehr January 1989 1 m ,m wang i
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APPROVAL SHEET This thesis is submitted in partial fulfillment of the r
requirements for the degree of Master of Science (Nuclear Engineering)
AUTHOR This thesis has been read and approved by the Examining Committee:
Thesis adviser Committee Chairman Accepted for the School of Engineering and Applied Science:
Dean, School of Engineering and Applied Science January, 1989 i'
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- . ACENOWLEDGEMENTS
[ The author would like to acknowledge the contributions of UVAR staff member Dave Freeman whose follow up and support calculations provided much confidence in the work 1
presented here. Many thanks are also due to all of the people who have provided assistance and guidance along the way including (but not limited to): Dr. Roger Rydin, Dr.
Robert Mulder, Stuart Wasserman, Bo Hosticka, Pres Farrar, knd Vance Hampton (for keeping the Genicom printer going through all of the computer runs done) . A very special "no thanks" goes to Roger Johnson for the continual reminder of all of the trees that were sacrificed for this project.
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L 11 ABSTRACT s
The HEU-L2U fuel conversion effort at the Univers.ty of
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Virginia for the 2 MWT UVAR reactor was divided into several areas of concentration. This portion was concerned primarily with scoping studies for the neutronics calculations and design. Computer models were created and tested to. determine'the capabilities of the codes being used with respect to the objectives sought for the UVAR. Three fuel configurations (HEU 18 plate / element curved plate fuel, i
LEU 18 plate / element fuel, and LEU 22 plate / element fuel)
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were studied in depth. These studies included the testing of each fuel configuration in each of three core configuration models (4 x 4, 4 x 5, and 5 x 5 arrays of fuel j elements). Control rod worths were determined for each fuel configuration for the beginning of life 4 x 4 core, and these cenpared very favorably with experimental measurements made of the HEU BOL core in 1975. Depletion studies dona follow trends set at other institutions, and indicated that ;
the LEU 18 plate / element fuel is nominally a direct replacement for the existing HEU fuel in the UVAR for the 4 x 5 core array, although it maintains a lower excess reactivity throughout its life than does the HEU fueled core. These studies also showed that the use of 22 plates / element in the 4 x 5 array would provide a
4
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iii considerably longer core life time as well as a generally I
s", .hi gher thermal flux than ei ther the exi sti ng HEU e l ements or the LEU with 18 plates / element.
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- 1. INTRODUCTION . . . ................. 1 1
1.1 BACKGROUND
OF STUDY . ............. 1 1.1.1 Purpose of Conversion and Study ... 1 1.1.2 Characteristics of the UVAR ..... 2 i 1.1.3 Goals of the Conversion ....... 4 1.2 CODES TO BE USED .............. 7 1.3 VERIFICATION' ................ 8
- 2. PROCEDURE . . . . ................. 10 2.1 OBTAINING BENCHMARK CALCULATIONS ...... 10 2.1.1 Documents .............. 10 2.1.2 LEOPARD Model ............ 10 2.1.3 2DB Cell Model . ........... 16 i
2.1.4 2DB Core Model . ........... 21 2.1.5 Other Variables ........... 23 2.1.6 Mesh Spacing . ............ 24 o
2.1.7 " Card read" Cross Sections . ..... 27 2.1.8 Fine Tuning ............. 28 f
2.1.9 Verification . ............ 31 2.2 THE LEU MODEL . ............... 33 2.2.1 Fuel Specifications ......... 33 2.2.2 LEU LEOPARD and 2DB Models . ..... 34 2.2.3 Boron impurities . .......... 35 i
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2.2.4 22 Plate Elements . . . . . . . . . . 37 2.2.5 Results . . . . . . .. . . . . . . . . 39 2.3 OBTAINING CORE LIFE CALCULATIONS . . . . . . 40 j
2.3.1 Methods of Burnup . . . . . . .. . . 40 2.3.2 Depletion Cross' Sections . . . . . . . 41
- 2.3.3 Control Region Cross Sections . . . . 42 2.3.4 Calculation of Uniformly Shuffled Depletion . . . . . . . . . . . . . . 43 2.3.5 Calculation of Unshuffled Depletion . 44 2.4 CALCULATIONS FOR INCREASED CORE SIZES . . . . 45 2.4.1 4 x 5 Core Model . . . . . . . . . . . 46 2.4.2 Deplution and Results . . . . . . . . 47 2.4.3 5 x 5 Core Model . . . . . . . . . . . 48
- 3. RESULTS AND DISCOS 8 ION . . . . . . . . . . . . . . 50 3.1 BENCHMARK CALCULATIONS . . . . . . . . . . . 50 3.1.1 Basic Data . . . . . . . . . . . . . . 50 3.1.2 Control Rod Worths . . . . . . . . . . 51 3.1.3 Beginning of Life ker e . . . . . . . . 53 3.2 4x4 CALCULATIONAL RESULTS . . . . . . . . 55 3.3 4X5 CALCULATIONAL RESULTS . . . . . . . . 57 3.3.1 Depletion Methods . . . . . . . . . . 57 3.3.2 Axial Buckling Trials . . . . . . . . 59 3.4 5 x 5 CALCULATIONAL RESULTS . . . . . . . . . 62 3.5 ADDITIONAL HEU TO LEU COMPARISONS . . . . . . 63 c.
vi
- 4. CONCLUSIONS AND RBC080tRNDATIONS .. . . . . . . . . 68 y
4.1 CONCLUSION
S . . . . . . . . . . . . . . . . . 68 4.2 RECOMMENDATIONS . . . . . . . . . . . . . . . 72
- n 74 4 5. FUTURE WORK ON TEIS rROJECT . . . . . . . . . . . .
T appsNDI . . . . . . , , . , . . . . . . . . . . . . . 77 lt ..
80 REFERENCES . . . . . . . . . . . . . . . . . . . . . .
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vii LIST OF FIGURES Figure 1. Standard Fuel Element for LEOPARD Input . . . . . . . . . . . . . . 12 Figure 2.
Control Fuel Element for LEOPARD Input, by Region. . . . . . . . . . . . . . 13
- i' Figure 3. Control Fuel Elemant for LEOPARD Input with Lattice and Non-lattice Regions. . . . -. . . 15 1
Figure 4. Standard Fuel Element with Curved Fuel P Plates. . . . . . . . . . . . . . . . . . . 16 4
Figure 5. Control Fuel Element with Curved Fuel
- - Plates. . . . . . . . . . . . . . . . . . . 16 Figure 6. Grid Plate Measurements of Fuel Cell. . . . 20 3
Figure 7. Standard Curved Plate Fuel Element. . . . . 20 Figure 8. Standard Fuel Cell in 2DB. . . . . . . . . . 20
,1 Figure 9. 4x4 Core Model. . . . . . . . . . . . . . 21
,. Figure 10. 2DB Fuel Cell with Mesh Spacing. . . . . . 26 Figure 11. The Effect of Mesh Spacing in the Reflector Region on k tr. . . . . . . . . . 30 Figure 12. 4x5 Core Model. . . . . . . . . . . . . 47 I
Figure 13. 5x5 Core Model. . . . . . . . . . . . . 48 Figure 14. Reactivity of 4 x 4 Cores Over Time . . . . 56 Figure 15. Reactivity Over Time for 4 x 5
- g. Uniformly Shuffled Cores. . . . . . . . . 58 Figure 16. Reactivity Over Time for 4 x 5 l' Unshuffled Cores. . . . . . . . . . . . . . 58
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- Figure 17. Reactivity Over Time for 4 x 5 Cores Using
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L 1st Buckling Approximatwn. . . . . . .. . . 60 Figure'18. Reactivity over Time for 4 x 5 Cores Using 2nd Buckling Approximation. . . . . . . . . 60 Figure 19. Reactivity over Time for 4 x 5 Cores Using 3rd Buckling Approximation. . . . . . . . . 60 Figure 20. Reactivity Over Time for 4 x 5 Cores as Calculated by ANL. . . . . . . . . . . . . 60 Figure 21. Reactivity of 5 x 5 Cores'Over Time. . . . 63 Figure 22. Thermal Flux Traverse in the Direction Through the Fuel Plates and Through the Peak Flux Value in the Fueled Region. . . . 64
' Figure 23. Reactivity of 4 x 4 Cores Scaled to the Life Time of 4 x 5 Cores. . . . . . . . 65 Figure 24. Reactivity of 4 x 5 Cores. . . . . . . . . 66 Figure 25. Reactivity of 5 x 5 Cores Scaled to r the Life Time of 4 x 5 Cores. . . . . . . . 67 Figure 26. Long Core Experiment. . . . . . . . . . . . 77 Figure 27. Sample EPRI Core. . . . . . . . . . . . . . 78 Figure 28. Ground Floor View of Reactor Face, Pool, and Approximate Position of Core. . . . . . . . . . . . . . . . . . . . 79 P
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l I. .ix LIST or TanLas 4.
Table I. Basic Fuel Element Data. . . . . . . . . . . 35 Table II. Control Rod Worths for the 4 x 4 Texas A&M Core and Replacements. ....... 6 . . 52 Table III. Beginning of life Unrodded k.tr for 4 x 4 I' Texas A&M Core and Replacements. . . . . . 54 B, -
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- 1. INTRODUCTION h
1.1- BACKGROUND OF STUDY 1.1.1 Purpose of Conversion and Study The University of Virginia, with support from the Department of Energy (DOE) and assistance from Argonne National Laboratory (ANL), is studying the effects of converting the university's two megawatt swimming pool research reactor, UVAR, to low enrichment fuel. The conversion of almost all domestic, non-power reactors to low enriched uranium (LEU) is part of a U.S. policy [1] geared toward reducing the risk of nuclear weapons proliferation. One of the goals of the Reduced Enrichment Research and Test Reactors (RERTR) program was to develop, test, and promote the utilization of a fuel that had a much lower enrichment of uranium than the standard 90% to 93%. A second goal was to develop a fuel that would be almost a direct replacement, from both a thermal-hydraulic and a reactivity point of view,for the high enriched uranium (HEU) fuel.
I The LEU fuel element which resulted from the various goals was one which had a lower enrichment (about 20% U-235), a 15% higher loading of U-235 per element (225 g versus 195 g), a much higher uranium density per element (3.47 g/cc versus 0.69 g/cc), and approximately the same dimensions as the HEU fuel element. The dimensions and
i' 2
loading of the University of Virginia's fuel plates were s chosen to_ serve as the standard plate for all U.S. research
[ reactors (2). It should be noted that while all institutions choosing the plate-type LEU fuel will be using the same standardized fuel plate, the number and spacing of f
these plates within the fuel element will vary between these institutions since their element specifications are different. (Two other. options open to U.S. research reactors seeking to convert to LEU are to meke use of the SPERT fuel pin or to convert to a TRIGA reactor core, however these options were not studied by Virginia).
1-1.1.2 Characteristics of the UVAR Throughout the past 28 years, the UVAR has been strictly an experimentally operated reactor. This means that the shape and size of the i
core as well as the core laading pattern and boundary conditions were easily varied over time as the need arose.
Some examples of past core configurations may be found in I the Appendix. Each time a new core configuration was loaded, it had to be tested to assure compliance with the safety Analysis Report (SAR) and Technical Specifications (Tech. Specs.) with respect to excess reactivity and shutdown margin. The number of fuel elements used in a
- j. given core would vary between 16 and 27 as the core depleted. Partial elements, those in which every other fueled plate is removed and replaced with an aluminum plate,
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3 were also used. In addition to the standard 18-plate curved k, plate' elements, the UVAR grid plate has been loaded with 12-plate, flat plate element cores. Complete cores (of either 18 or 12 plates per element) would have to alternate in some fashion between these two types of-elements so that all elements would remain self-protecting. (An element is considered to be self-protecting if it measures 100 R/hr at 1 meter in air.) Given all of this, there has never been a i:
set core loading scheme. The cores were always loaded to g
meet all of these types of needs, with an attempt to start each new configuration with approximately uniform burnup.
1 Rough burnup records for each element were maintained, and from this, judgement was used to determine which elements I
would be placed in any given position.
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control is maintained in the core by the use of three
, boron stainless steel shim rods and one stainless steel regulating rod. Each rod is located within a control rod i element. The control elements are positioned in a staggered pattern throughout the central portion of the core so as to allow the emergency core spray system uniform flow access to the entire core, without interference from the control rod drive mechanisms.
I The UVAR core is comprised of elements positioned on a i grid plate suspended near the floor of the reactor pool.
- . - - - - - - - _ ~ _ _ _ _ _ _ _ _ - _ _ ~ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _m______._________,__.,_____._____ _______ _ _ , _ _ _ , . , _ _ _ _ , _ _ , _ ,
j L1 4 The grid plate has 64 positions available for fuel elements, 1
graphite elements, and various experimental facilities.
I; , These 64 positions are arranged in an s x s array. The i
l core is moderated by water and reflected by water and/or f
I graphite. Graphite elements are approximately the same size !
I as standard fuel elements, and fit into the grid plate holev 1
in the same way that all the other elements do. Thus, the 5 amount and the arrangement of the graphite around the core is limited by the position, size, and shape of the core, as v'11 ** bY th* capacity of the grid plate. The amount of T
graphite may also vary as the core burns and new elements
,I are added to the core so that the core will remain within Tech. Spec. limits of operation.
I In addition to having water and/or graphite surrounding I
the core, a variety of experimental equipment might also be l placed next to or inside the cora at various times as,.i for.
varying durations over the life of the core. At this time, I one face of the core can be used for fixed or removable experimental facilities. Different experimental facilities that have been used over time may be found in core diagrams located in the Appendix.
.g 4 1.1.3 Goals of the conversion In addition to the order to convert to LEU fuel, all affected facilities were also 0' asked by the Nuclear Regulatory Commission (NRC) to avoid I
5 making any changes to the reactor, outside of direct replacement of the core, to a minimum. For this reason, the
[ University of Virginia decided to study the new fuel type, and determine whether a simple direct substitution of fuel I elements would maintain, reduce, or improve the current level of operation of the UVAR experimental facility. The I
primary interest was to maintain, as a minimum, the current level of experimental flexibility. If greater flexibility I
could be gained, that would be desirable, however a loss of flexibility would not be looked upon in a favorable manner by the experimenters at the UVAR facility.
A second point of concern was the (reactor) staff practice of increasing the size of the UVAR core as it burned. At the beginning of core life (BOL), the core i .
consisted of sixteen elements (four of which were control elements), arranged in a 4 x 4 pattern. As the core burned,
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in order to keep sufficient excess reactivity, full or I partial elements would be added. At the present time, the core has 26 elements (including the four control elements).
By increasing the core size in order to extend core life, the higher leakages associated with smaller cores and higher average thermal fluxes were sacrificed. Obviously this is not desirable for an experimental facility which relies very heavily on leaked neutrons for its livelihood. It is for this reason that additional studies were done toward 1
1' 6 maintaining a more compact core. A 4 x 5 core seemed to be l
the most reasonably maintainable core, and so this core was studied in detail.
l The final major interest for the LEU fuel conversion study was that the new core should be able to accept a wide range of experiments placed on its boundary. These boundaries include conditions that have been utilized with past cores, as well as various potential experimental upgrades. Some of these boundary conditions includes one, two, or three open beam ports at a timer a rotated core I allowing for symmetrical control rod placement, with two faces open for removable experimental facilities; and an experimental flux trap within the core.
Since all computations to be done required the use of computer codes for modeling the'UVAR core, the computational models had to be benchmarked with experimental :seasurements.
Benchmarking was done by modeling the first 18 curved plate element core utilized in the UVAR (referred to hereafter as the Texas A&M core or just the Texas core), and comparing the modeling results to actual measured results. The Texas core was chosen for benchmarking purposes since it was the only core configuration for which exact values were known for the weights of the individual elements, for the loading of these elements, and for the burnup of these elements.
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The Texas core was also probably one of the best documented cores in terms of experimental measurements taken for the !
g purpose of licensing requirements. One final plus for the Texas core was that it was perhaps the " nicest" core that I could be used from a symmetry point of view. l
, 1.3 CODES TO BE USED j
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All modeling was to be done using computer codes that !
I t i were operational on the University's CDC Cyber 855 mainframe j g
computer. Codes already in operation at UVA included f THERMOS, GAMTEC, EXTERMINATOR, and RETRAN. THERMOS is a i i one-dimensional thermalization code utilizing transport [
theory for its calculations. It has available slab and cylindrical geometries for description of the cell. GAMTEC l is a one-dimensional transport code that is a combination of I !
the GAM slowing down code and the TEMPEST thermalization j l
l code. GAMTEC is separable in energy and cylindrical space.
EXTERMINATOR in a two-dimensional few-group diffusion theory >
code. While it does not have the capability of performing depletion calculations, it does have the ability to do modeling ef a single element without leakage creating a E,g numerical convergence problem. RETRAN is a theranl-hydraulic analysis code for an entire reactor system.
Computer codes which were received from ANL through the l0 University of Michigan included LEOPARD, LINX, 2DB-UM, and 1 _ ___ -
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the PARET package. LEOPARD is a zero-dimensional, slowing l
down and thermalization, cross-section generating code that has the ability to do cell depletion calculations to obtain these cross sections. Calculations may be done using either 4 two or four energy groups. (At DVA, two energy groups were )
used in calculations. It was later announced (3) that when f
' using LEOPARD as the cross section generator, the two group !
calculations were found to be more accurate at predicting 6 ,
the behavior of'several small university reactor cores than j l
the four group calculations were.) LINX is a convenient i means of transferring the cross sections generated in 9 LEOPARD to 2DB. 2DB, the final neutronics code in the i package, is a two dimensional, diffusion theory code used to .{
model the core itself. It allows for input point depletions i to be done directly from the LEOPARD table, or it will carry out spatial depletions for the user once given the starting i I, point of the depletion study and the time steps to be taken.
r It will calculate almost all neutronics parameters of i
- interest. The PARET package is a collection of thermal hydraulics codes.
t 1.3 YERIFICATION The verification of the methods used in this part of a the project was restricted to the comparison of the ,
effective multiplication factor k.rr, and the rod worths for the calculated versus measured benchmark case. Some degree f - _ _ _ _ _ __ _
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' . 9 of verification was also available by demonstrating that the i
LEU fuel would follow certain established trends. The only I
g trend worthy of note here was that the LEU should be roughly j equivalent to the HEU by the end of the core life (EOL) (4). j i It is important to note at this time thht EOL for the UVAR is not a very specifically defined term because as the core I
depletes and excess reactivity and flux levels are no longer !
high enough to support experimental work, more fuel elements .
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are added to the core to keep it going for a longer period i I; of time. It was 1rter determined that the fuel developers considered the EOL for the UVAR to be the point at which a 4 i x 5 core no longer had sufficient excess reactivity. l i
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- 2. PROCEDURE i :
t I 2.1 OBTAINING BENCEMARK CALCULATIONS g
3.1.1 Documents In order to properly model the Texas l- core, all of the original data.for the Texas fuel needed to j be found. Since the Texas core was first put into operation
'I
! in 1975, nost of the data was found in files labeled " Texas II
'75" or " Texas A&M" core and fuel (5). Almost all of the required blueprints of the fuel plates and elements were {
i g found in the blueprint file (6-8), however any that were missing that contained necessary information were replaced I by blueprints from the next generation of fuel, known more !
commonly as TRTR-2 fuel (9-11). This TRTR-2 fuel was essentially the same as the Texas fuel, so only where necessary, important data was taken from these documents and used as Texas data, l.
2.1.2 LEOPARD Model Once all of the basic pertinent
'I data (dimensions, weights, loadings, etc.) were obtained, it ;
was possible to create a LEOPARD model (12). Since LEOPARD is a zero-dimensional code, all of the information that was input to describe the model was done with respect to a basic :
cell. This basic cell is comprised of everything that a l standard element is comprised of, and yet all information '
about this cell is given in relative values. For instance, ;
in describing the fuel meat itself, all values are given as 9 . _ _ _ . _
)
l 11 l either number densities or volume fractions. The cell composition part of the input to the code is broken into
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"I, four parts. The first part is the description of the fuel j meat, the second describes the clad material, the third the a moderating agent, and the fourth describes everything else i b (primarily the structure of the element and anything " extra" l
' in the basic fuel-clad-moderator cell). The first three parts are lumped together and called the lattice region, l
,.4
! while the fourth part is referred to as the non-lattice region. The meat region must contain a fissionable isotope, g
f and cross sections are generated for the lattice region l
1 using the spectra of this fissionable material. Cross ;
sections are generated for the non-lattice region by using a
" borrowed spectrum" from the lattice region. The relative f strength of this borrowed spectrum is directly dependent on !
I an input factor referred to as the non-lattice fraction, f
1.e., the fraction of the basic cell that is in the non-l lattice region. [
.I ;
There are two basic types of fueled elements which are 1' i dealt with in this study, standard elements and control rod l elements (known hereafter as control elements). Thus there are two sets of LEOPARD input decks that are needed to a properly describe each different region. First, the input i for the standard element will be described, followed by that for the control element.
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12 i The composition input is broken up into fuel, clad, I t moderator, and extra regions. The fuel is made up of either UA1,-Al alloy or U,sia-Al (in the case of the 120 fuel), and i its dimensions set the basic size limits for the rest of the i regions. The clad is defined as the aluminum that is ,
immediately on either side of the fuel; it does not include 3
any aluminum that extends beyond the meat edges. The ,
I moderator is the water immediately on the outer sides of the t
Any other water or clad material that extends beyond I
clad.
g the edges of the meat, as well as any additional water or j box structure on any of the ends, is considered to be in the Figure 1 gives an idea of the way the model i extra region.
is defined, with region 1 being the fuel-clad-moderator f region, and region 2 being the non-lattice region. f DM/f((f/f(( REGION 2 f I I '
I f fJf f[1fI '[ fff j i
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- i ! i REGION 1
! t i
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tkI k l k k lII Lk MN REGION 2 ;
Figure 1. Standard Tual Element for LEOPARD Input i
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The control element is the same as the standard element except that half of the total number of fuel plates are j Ig reroved from the center of the element to make room for the l control rod and its guida plates. For this type of element, i there are four basic regions (see Figures 2 and 3). The l first two of these regions, the fuel and its associated clad
! and moderator (region 1), and the edge and box structure extra region (region 2) are defined as above for the j I
standard element. The cross sections used are the same as those used above. The other two regions (regions 3 and 4),
g those corresponding to the first two regions but in the i i
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center of the cell, are somewhat different because the fuel plates are now replaced by guide plates, water, and either l control rod or control rod water. (Control rod water is v i taken to be that water which replaces the control rod when I i the rod is removed.) ;
REGION 2 RE010N d REGION 2
)71hhT r
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REGION I REGION 3 RE010N I ,
i t L < L L L t l !
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l RE010N 2 REGION 3 REGION 2 Figure 2. Control Fuel Element for LEOPARD '
Input, by Region.
g 9 _
.. ::= := : - - - - - - - -- -
14 !
Since neither of these two regions, (3 and 4) contains fissionable material, " borrowed" spectra must be used, and i thus these are also considered to'be non-lattice regions.
The size of region 3, the control box, is that which is i
'; vacated by the removal of half of the fuel plates, i.e., it ;
, extends out to the edges of the seat and is the width of the l
' removed plates with their associated water moderator. This !
! region contains the control rod guide plates and water. -,
g (Effective cross sections for this region for the case of a !
l.. control rod or regulating rod are calculated elsewhere by {
Wasserman and Freeman (13,14).) The lattice region is as ,
defined above for a standard element, while the non-lattice j region is defined by the control box. The non-lattice f fraction is thus 50%. The final region of interest, the [
edges of the control box (region 4), includes the edges of the guide plates and ths water between the control box and Ia the side plates of the element, as well as the side plates and extra water within the boundaries as determined by the l 1 remaining fuel plates. The aluminum and water volume fractions within this region are very close to those found within the corresponding region for the standard element, and since both must use borrowed spectra, it was decided to I l use the region 2 non-lattice cross sections generated for l T the standard element for this region as well. f In summary, the control element is subdivided into I
1 :
15 three regions requiring different sets of cross sections.
The non-lattice region (region 2) of the standard element I
i g
corresponds in both size and approximate volume fractions to l the edge region of the control element. The fuel regions >
(region 1) in the two types of element use the same number densities and configuration, and thus both have the same I cross sections. The control box (region 3) must be treated l separately, and it is designated as the non-lattice region :
4 !
in the control rod LEOPARD calculation. The input buckling g
was taken to be that value valid for the entire core, and was obtained using an estimated reflector savings based on f
4 the transport extrapolation length. The active volume and i power, required for depletion calculations, were taken on a ,
I per full fuel element basis to give the correct average f power density of the core. !
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PON* LATTICE 7
LATTICE
!I l 1
_ _ h NON L ATT ICE LATTICE NON LATTICE LATTICE Figure 3. Control Fuel Element for
.Il. LEOPARD Input with Lattice and Non-lattice Regions. ,
.- .- :- _:: = w : - - - ---
i l
16 ;
3.1.3 3DB Cell Model In modeling the fuel cell for the 2DB code (15,16), special care needed to be taken since the !
I, 10 plate fuel element was made using curved plates rather l than flat plates. (Compare Figures 4 and 5 below with
( Figures 1 and 2 or 3.) {
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Ig Figure 4. Standard Fuel Element with Curved Fuel Figure-5. Control Fuel Element with Curved Fuel Plates. Plates.
I The procedure developed to design the 2DB cell is 1
illustrated below and is based on conservation of area in the two-dimensional cell.
LII" As a starting point, the outer size of the element, and ,
thus the size of the 2DB cell, is given by the " center-to- i center" dimensione of the holes in the grid plate which t T holds the elements. These dimensions were taken from blueprints of the grid plate and subsequently confirmed by ,
I actual measurements performed by reactor staff members (17).
l.
a Y - _ -
17 In Figures 6, 7, and 8 as well as in the discussion that follows, these dimensions will be referred to as G , for the direction through the plates, and G,, for the direction along the fuel plates (refer to Figure 6). (The axial, or J
4 "z" direction is not explicitly used in these calculations.)
The area found when G, is multiplied by Gy is given by Ao.
' 3 The second " fixed" dimension was taken to be the width of a fuel-clad-moderator ensemble. This is the width of the j a
, lattice region in LEOPARD and is the pitch of the fuel l g
plater it is referred to as L, in Figure 7 below. The width !
(L,) and length, L,, of the lattice region of the fuel plate !
t may be combined to give A t , the area subtended by the fuel- !
clad-moderator ensemble of a plate in the standard fuel
' I !
element.
I i
The fueled (fuel-clad moderator) region of the olement is the single most important region in the model of the cell !
and core in 2DB, so care is taken to maintain it as l I unmodified as possible in the model. For a standard, 18 plate element, the lattice region in LEOPARD is given by 18 times the area A t. Recall that the non-lattice region is defined as everything else in the call that is not specifically defined as lattice. Thus, the area of the non-lattice region is that which remains when the 18 At is subtracted from the area subtended by the grid plate 8 dimensions, Aa. The non-lattice area is given the I _ _ . ____ - .
l 1
, 13 designation Art.i (Refer to the equations next to Figure 7.)
l t.
This area is also maintained in the 2DB cell. (See Figure l l l l
cp 8.)
l i When actual numbers are applied to the above '
description, it is found that G, is slightly larger than 18 times L,. This is due to a small amount of water
, surrounding each element, and allows for easier movement of ;
1
' an element in or out of the core (as opposed to the fit l
, y being " skin tight"). Since it is not practical to actually place water in this very small space in the 2DB model, the concept of conservation of area was used to take care of the l To achieve this, the length G, was divided into 18 I problem.
equal lengths, each of which was designated L,'. The area, !
At was then divided by L,' to give a new length L,' for the j lattice region. Since each L,' represents the width of one j " plate", in order break up the standard cell model so that 1 it might also be used as the control-cell model, the plates !
were grouped into three groupings, one for the control box, and one for the block of fuel plates on each side of the i control box. Thus, from the leftmost part of the cell, the divisions are 4 L,', 9 L,' , and 5 L,' accordingly. ,
With the new dimensions now defined (L,' and L,') for the 2DB cell fueled region, only the non-lattice structure region of the cell remains undefined. Again, area is
'i ei 19 I conserved, as the area An is divided by G, to give the width 4
of the modified structure region. This width is then i divided by two (one for each side plate structure region) . l l
This value is then labeled NL,' in Figure 8 below.
o t I,
l
.)-
)
lI.
l t i
b P
I q
~ . - ... ... .-- . .. . . . . . -.
p
, r 30 \
i G,
.g4i. A, = Gx
- Gy .[
5-g i
'E i :
- 3. .i G, i. j Figure 6. Grid Plate Measurements of Fuel Cell. ,
a.
t At= 4*4 A,t = Ao-18At f
amauama H
be !
t i
- Figure 7.
Standard Curved-Plate Fuel Element. !
' t
[
T >
NL s- s' l 4' - Gx/is Lv 4 ' - Av4 ' l 2N4' = Am/Gx .[
NLy {
_L I
! 18 L, l i
Figure 8. Standard Fuel ,
Cell in 2DB.
I
- '1' q y 7g- -w-g '
c . . . . , . . . -
i E8 21 :
2.1'.4 3D3 Core Model The 2DB core model is made up of f
1
.~
reflector material and the appropriate number of basic cells ;
which were developed in detail above. The core itself is l t
comprised of 16 basic cells in a 4 x 4 array. This is then 3
surrounded on all sides by the equivalent of three cells of ,
reflector material. This reflector material is water on the
- outside of the model, and " canned" graphite (8) on the inner
. part of the reflector immediately next to the core itself.
Figure 9 illustrates the basic configuration of the Texas l 6 core model including the relative thicknesses of the two l
}L l types of' reflector material. -
l t
I
.._._m_ _ _ .. .m
.I _~ _
e i ,
T 5
- **M .
- +M .r j d 2 1 s >
t:
3 .-
wa 3EE GRAPHITE WATER I
- mt I- Figure 9. 4x4 Core Model.
I e
g -. . .. - -. :n.- ~~~ ~
3 4 22
- since the grid plate on which the core and graphite '
s elements are loaded is an 8 x 8 element unit square, the amount and positioning of the graphite reflector about the !
core is limited. Of course, less graphite than the maximum I6 amount possible may be used, however this decision is based l
on the needs of the facility at the time as well as on ,
' operational regulations. A lesser amount of graphite around the core any be considered a change in core boundary conditions and thus is not dealt with in this study. !
I6 The Texas core is made up of 16 basic cells. A cell is a considered to be a squared-up version of an element; the ,
I cell takes up the same area as the element, however it is ;
slightly modified so that x-y geometry might be easily used.
The fuel cells are divided as indicated above in Figure 8, 4
while an explanation of the mesh spacing appears in Section j Ig 2.1.6. All structure regions use the non-lattice cross ,
sections calculated with the standard element in LEOPARD. ,
( All fueled regions in both the full fuel element and the control element use the lattice cross sections from the
' The center section of the element might standard element. ;
contain fuel, a control rod, a regulating rod, or a water 1 .
hole representing the absence of a rod. Fuel cross sections ,
. i are obtained from the lattica region of the standard fuel element. Effective control and " reg" rod cross sections ,
a were obtained from work done by Wasserman (13) and Freeman 1 _ _ _ _ _ _. - _ __ _
s P 23 i
(14). Cross sections used for the water hole were those obtained as non-lattice cross sections in the control fuel l; I,
element. l 3.1.5 other Variables The majority of the input into the j 2DB code either describes the model of the core or gives
' instructions to the code about the types of calculations and !
output that are desired. Exceptions to this include such 1
information as the power modifier, the volume involved, and the axial buckling of the core. Most of these are simply basic calculations that require nothing more than plugging l8 in the appropriate numerical values when required. An exception to this statement is the case of the axial l#
buckling. For this, as a first approximation, an extrapolation distance of 4.5 cm was added to each end of I i ;
I the active core, and the axial buckling calculated as usual. !
3 The value of 4.5 cm may most correctly be referred to as a j judgement call since there are no well documented values to ;
r
- i. "
l be used in this case. This value was found to be approximately what was required for the 2DB results to match l t
experimental results, and it seemed to be approximately that !
determined by J. L. Mesa in his two-group calculations for ,
a the original UVAR (18). It was later determined that use of I~
6 an incorrect definition of reflector savings contributed to '
this (mis)matchup between Meen's value of 8.65 ca for 8
reflector savings to be added to the height of the core at ;
! i 24 both ends and the value of 4.5 cm used in the calculations.
Sensitivity studies were done using a variety of values for l
the axial buckling, and it was determined that there was 9ssentially a linear relationship between axial buckling and l.
kort. Thus it may be used as something of a scaling factor. )i
! The second axial buckling approximation took into ,
consideration the problems discovered with the first approximation, and thus a value of 7.8 cm reflector savings ,
- I,
(
was used. This value agrees fairly well with values t i
L determined by.ANL using three-dimensional analysis of the i
[ a. UVAR (4), as well as with the va3ue obtained at UVA using an '
RZ model of the core, and it is not too far off from Meen's l " basic principles" hand calculations. l 2.1.4 Mesh Spacing Determination of the mesh spacing to be used in the 2DB model was rather simplified by the i
original design of the basic cell. Since 2DB is a diffusion theory code, it was not desirable to have the mesh spacing ,
be widely varying in nature. As an upper limit, the mesh sizing needed to be internally consistent in the x and y t directions, and it needed to follow the various boundaries imposed by the basic cell (e.g., the non-lattice region and I, the control rod region). As a lower limit, ultimately, !
practicality of calculation time was the only limiting l e
factor.
I.
e ,
s f
25 The decision of mesh space sizing was made fairly early in the modelling process. Since it was decided that at a
/ later time it would be desirable to be able to move the control elements to other positions in the core model, the mesh spacing for the standard elements was chosen to be the same as that for the control elements to ease this modification. For this reason, the spacing utilized will be described in terms of the control element, with the standard element being a subset of this.
In the "y-direction" (along the plates of the element),
six mesh spaces describe the element. Two of these spaces are for the non-lattice region (one at each end of the cell). The remaining part of the element (the lattice region) is divided equally between the other four mesh spaces. This is illustrated in Figure 10 below.
L In the "x-direction" (through the plates of the I element), eight mesh spaces were used. Since the control rod and its structure take up half of the element in this direction, half of the mesh spaces are devoted to it. (In the case of the standard element, these spaces are occupied by fueled plates.) The remaining four mesh spaces are g divided between the plates on either side of the control region, two on each side. Given the physical description of the element in the x-direction, it is easily seen why the
+-
26 decision was made to have the number of mesh spaces for this region be a multiple of four. Four mesh spaces seemed too few (especially in light of the fact that there would be only two describing that direction in the control region),
and eight mesh spaces made the dimensions of a square mesh space a lot more compatible with the dimensions describing this region in the y-direction. (In this way, the spacing was relatively similar in the x and y directions. Any great differences would have been inconsistent with the basic requirements of diffusion theory.)
NON-LATTlCE -- EXTRA REGION l
FUEL OR FUEL CONTROL ROD FUEL f
OR CONTROL ROD WATER h NON-LATTICE -- EXTRA REGION Figure 10. 2DB Fuel Cell with Mesh Spacing.
Since the cross sections for the control rodded region were determined using a combination of transport and i
I
N l
?.
I 27 diftesion theory codes, and in general were calculated in a much different manner than the other cross sections used in i the 2DB code, great care had to be taken to assure that the mesh spaces were comparable in each case. This was perhaps one of the strongest reasons for the choice of mesh spacing.
I 3.1.7 " Card read" Cross sections cross section values that were not able to be transferred to 2DB via LINX were required to be input by hand as " card" input. Most of the card read cross sections were not able to be calculated in LEOPARD due to the lack of any fissionable isotopes in the
) region of interest (the exception to this being the calculation of the cross sections in the control box region done as a non-lattice region in the control element run of f LEOPARD). There are five sets of card read cross sections 1
in the 2DB input. The five sets are comprised of reflector 1
water, reflector graphite, control box water, control rod, and regulating rod cross sections.
I Four of the sets of cross sections had to be calculated using methods other than LEOPARD for their generation. The two types of reflector material were in this category due to the lack of fissionable isotopes present within them, while i the two types of rod material required transport theory to appropriately model the strong absorber. For the canned I graphite (a graphite block placed in a sealed aluminum
~
j I 28 container), appropriate proportions of graphite, air,
+ aluminum, and water (between the elements) were determined,
[ and this information was used as input into the code GANTEC.
The output cross sections from GANTEC were then used in the 2DB core model. Cross sections for the reflector water might have been similarly obtained, however they were 8
instead received from ANL (19). These water cross sections were calculated using the code EPRICELL. The calculations a
for the rods were done at UVA using THERMOS, GANTEC, and
- EXTERMINATOR by Wasserman and Freeman. Canned graphite cross sections for the reflector region were also available i
i from EPRICELL (20), but were not used in these calculations i since they were essentially the same as those obtained and I
already in use at UVA.
I l
2.1.8 Fine Tuning The number of cells of reflector g material surrounding the core was chosen to be three on all sides, and this decision was based initially on a judicious guess. Having approximately nine inches of reflector surrounding a core that was approximately twelve inches wide i
in each direction seemed adequate at the time. It was later learned that other people involved in these sans calculations at other institutions were using similar i thicknesses of reflector material for comparable sized cores, and therefore the decision was upheld (3). Of course I the final decision lay in whether the addition of any I
y . . . . . - . - . .
L 29 additional amount of reflector material would change the I
output results of the code. (If the k% t calculated by 2DB with the original thickness of reflector material was the same, or approximately so, as that calculated using a larger thickness of reflector material, then the original amount i
was taken to be adequate.)
once the reflector thickness to be used in calculations was finally decided, the mesh spacing in those reflector cells needed to be determined, since there was no real idea as to what the appropriate spacing should be, it was decided to model a basic core and run several cases of this same model, altering only the size of the reflector mesh in each case. The resulting ker was then plotted against the number e
of spaces in the reflector region in the outward direction.
This plot is presented below in Figure 11.
As can easily be seen from the plot, the value of ktr is affectod very strongly by the size of the mesh spacing when that spacing is very large. The mesh spacing was chosen to be that spacing at which point k ort was no longer I
appreciably affected by changes in the spacing. According to the plot, k.tr is not affected much by using more than six or seven equal sized mesh spaces in the reflector region.
}
Since the three reflector cells could most conveniently be divided into six mesh spaces (two spaces per direction per l
30 reflector cell), this option was chosen over the seven meshes per reflector distance.
DEPENDENCE OF k OF MESH SPACING
.., w e. . .e,o.
$.s. I l , , .
4.5
, e. .
O 9 00 =
4.03 -
f g 4.o .
, . 0, .
103 =
1.08 = -
5 Os , , . , ,
9 3 S ?
es. amen fd 649H poseFS tu .E8L90f0R Figure 11. The Effect of Mesh Spacing in the Reflector Region on k.cr.
As discussed in the proceding paragraph, it was determined that, for any given direction, two mesh spaces per reflector cell (total of six for the region) were sufficient to describe the reflector region. Due to a misunderstanding between two of the project participants, a model was made utilizing six mesh spaces per cell (rather than per region). Since this sm, aller spacing allowed for more accurate mapping of the flux in the reflector region
- j. (where the thermal flux peak was assumed to occur due to the high amount of leakage from this small core), and yet did
l-Wl' > 31 not significantly increase the cost of the calculations, it il was permitted to remain throughout the remainder of the jt study. (Ultimately, due to sheer amount of calculations being done by the code, and since it had already been I determined that two mesh spaces per cell were sufficient, the reflector region was modelled such that the inner two reflector cells were split into six mesh spaces each, while the remaining (outer) call had three mesh spaces. This decision was also justified since the reflector in the rows i farthest from the core has relatively very little effect on what happens in the core, and thus, mesh spacing there is E
not so critical.)
I i
3.1.9 verification In order to verify the benchmarked g
case, it was determined that delta k (the difference in k between the all rods in and the all rods out cases) and rod I worths (delta k for each rod) would be calculated and compared with measured values. Since 2DB deals only with a i' two dimensional core model, a control rod may be considered to be either in or out of the core, and partial insertions cannot be accurately calculated. Given these restrictions, g delta k and rod worths could not be calculated in even approximately the same way as obtained experimentally with I an actual core, yet they have the same meaning as the values obtained by measurement and thus may be compared.
i The radial peaking factor is the final item to be found I4
, , . . . . ~
a i
i 32 l
l and used for verification purposes. This factor is calculated in this study, but is not utilized here. Rather,
'it is used as input into the thermal-hydraulics study. The "l
thermal flux radial peaking factor is defined as the highest id flux found in the fueled region of the core dividad by the average flux in the fueled region of the core. ;
Lg 4
lI of actual interest is the power production peaking *
' factor, however this value is not directly available from f
{ 2DB while the thermal flux peaking factor is. In order-to obtain the appropriate peaking factor value for later
-0 calculations, an assumption was made that the macroscopic j fistiion cross-section is constant, or approximately so, over I, j I the entire core and that power is directly proportional to +
g this macroscopic cross section times the thermal flux.
Thus, thermal flux is proportional to power, and the power l' production peaking factor is equal to the thermal flux peaking factor.
+
.p This definition of thermal flux peaking factor is I :
careful not to include any fluxes found in the control regions, the structure regions, or the reflector regions since power is not generated there and thus inclusion of
'I '
these regions would not pr duce an accuratt power factor.
2DB automatically calculates a flux map of tae entire core, 4
providing a flux value for each mesh space. A careful study I.
^
.c .
a
! 33 of this map, including outlining regions to be avoided, l
gives tho' peak flux value for the core.
1 The average value for the core is obtained through the l use'of an edit. An edit provides a relatively large amount of information including fluxes.for each region in its definition. Since it is desired to obtain an average flux over all of the fuel in the core, an edit is required such that all of the fuel in the cora is in one region, and nothing else is included in that region. The remaining regions of the. edit may be designed to include other i sections of the core as reason dictates, the only' restraint is that the entire core model must be included within the edit.
2.2 THE LEU MODEL 2.2.1 Fuel specifications Following the completion of the benchmarking process, the next core to be modeled was essentially a duplicate of the Texas core, only the new core used LEU fuel instead of the HEU fuel of the Texas core.
(It should be noted here that all of the LEU models described in this study at UVA use curved plate elements so that a direct comparison might be made with the 18-plate curved plate HEU elements.) The LEU fuel was composed of U 3 Sim, with the uranium content being 19.75% enriched l uranium-235. The LEU fuel plate is the standard plate i
I
. r,
1 r
l 34 adopted for this conversion effort by all facilities choosing to convert to plate type fuel. The standard plate is based on, and has the same outer dimensions as the UVAR HEU plate'that was considered in the benchmark calculat' ion.
The information regarding the dimensions of both the fuel and the plate as well as the actual loading of the plate was all determined at a meeting at ANL attended by many of the facilities involved in the conversion and the ANL representatives of the RERTR program (2). Other required information was obtained from TRTR documents, and again, Texas core blueprints were used as needed.
2.2.2 LEU LBOPARD and 2DB Models The LEOPARD cell model and the 2DB core model were defined in the same manteer as was used for the Texas core. Some modifications to 1..yat values were required due to the different fuel type and the slightly different meat dimensions. The meat thickness remained the same, however the length and width changed slightly. Table I (2,6,7,9-11,21-23) gives all pertinent basic information for both the HEU and the LEU fuels. The change in the width of the meat affected the size of the lattice and the non-lattice regions, and the change in the length of the meat in the plate had its strongest effect on the axial buckling in 2DB.
s . . _ - , . - . .
]
a{- '
35
. Table I. Basic Fuel Element Data.
] .} -
,4
]
LEU-18 : LEU '
DESCRIPTIONL ;HEU-18
(,1E' p y, ,' ; 9 ;t ' ~.' m y ,' ,,, y/ 4 '
d.. Y ._ ..
- ' s
- +
u , , '8 IDimens'ional (incties) :i '
'3' .s 4 . .
g~ k./ ;', , . '
l [ W ,' . ? 6 '
$; ' I
'23.25lf'
, Active .. Length: 123.5 ,
- a c'.'23.25i's ;t.; ,, -
+
- ' c. ' , , , . .,..~ , .
'g
'E "b 2'395['l p ;. Width .c 2;375{ 72.395.c ,
3; $.
en ;
t i i
{Q pth; -
y0.02 ;0.02 ] '
L 0. 02.' j
,3 . . .,..;, - .. '
224.625 i' E
g Plate Length,' 24.625L<
~243625'
- W i:
g b' C- ' ., ..
'd ' Depth. J 0. 051 , 0105' .% ' + .0.05-L L- ,? t ,
,M n
41.114%_,y; '
- s> .. ., .9 s
. ,- . .. , , .3,116'
- Active: Volume (in;s) . .c1'.114 !
t ,y '~. .7 i
.. W ...v
- U-235/ element f(g)-
- 192.3* i ;~ 225'. #
275'
[5- ..',- ,
1
- l. ,
i.'. ,/. ' .x..
4
- U-235/ plate y(g) '
10.'68~, ; 12 7. 5 G ,
112.5".
4
, y. . '
U-238/plateL;- (g) [
j~ 0.81. 49[84 49.'84' ;
b .1:/.
f ,U-234/pla'te- )(g)5 . 0. 01 ,; ' O . 317; '
[0.317.
1,.. . t . .., .. . ..
I U-236/ plate ..(g). O.0 O.633 .0.633 >
s .
g N-2356 1oadingl(%) [ 9'2.92 19.75(
4 19.75'
> . m . ' . ', : .. .?' .s ;
I Water Gap 1(in'.)/ l0.122 0;122'"
0.091~
I. >- ,
,. rM. . , , :.,
,a <
a= ::,
.;w . . :n y(
'* " NOTE:
, 'This?is}the actual ~value'for the:approximately '
i
- j. i1%. burned fueloas; reported-by and receivedt from Texas.. _ .
- A&M .:in 1975 4 - . '
, , is gr. , , ,
M ,p :q ,
q J- 5 > < 3 ,
f p; ,
- I l '.
2.2.3 Boron impurities Much of the aluminum used in :
'[
the fuel elements is not considered to be pure aluminum (ni-I 24). In general, the two types of aluminum used are I.a
ft l8= 36 classified as Al-1100 and Al-6061, with the 1100 being.
essentially pure aluminum and the 6061 having a variety of
- 5 ,
impurities. (For the purposes of this project, any substance present in the Al-6061 that is not pure aluminum L is considered to be an " impurity", even if its presence is intentional.) some of the " impurities"'are actually ll alloying materials added to the aluminum, while others of ;
the impurities are the result of the fabrication processes a.
used. For calculational and design purposes, the impurities g are combined to give a " boron equivalent" impurity. This is done when dealing with reactors since boron acts as a poison a and will thus.have an effect on.the operation of the reactor. By referring to the impurities by their boron
' equivalent, their effect on operation may be fairly accurately determined.
.s l LI- p For calculational purposes, aluminum 1100 is considered
- to have no boron equivalent impurities, while the level of O impurities in the 6061 varies according to when and under ;
what conditions it was manufactured. For these a '
calculations, the 6061 in the HEU elements is considered to be more pure than that in the LEU elements. For the HEU elements, a value of 10 parts per million (ppm) was used.
- s This value is considered to be an upper limit, however a !
j more accurate value could not be easily obtained since it is A
difficult to accurately measure amounts less than this. For 9
i l.
3 '
37
- the LEU elements, a value was difficult to obtain since the i- .
! manufacturers were only given an upper limit of 30 ppa.
L Based on studies done, ANL suggested a value of 20 ppm be ,
used for these calculations (4). Even a value such as this is probably higher than what is actually found in the !
aluminum, however it was suggested as a fairly interme'diate l~' value between the probable and the upper tolerable limit. 1 Referring now to the LEOPARD cell description in section 2.1.2, for the HEU element, all aluminum in the fuel
- meat as well as all clad material is taken to be aluminum 8 1100, while all of the structure material (that in the extra, non-lattice, region) is considered to be 6061 aluminum with 10 ppm boron equivalent impurities (6,7). The ;
LEU element is similar, however, instead of the clad material being 1100 as for the HEU element, it is 6061 I' aluminum (4). All 6061 aluminum in the LEU element is considered to have a boron equivalent impurity of 20 ppm.
2.2.4 22 Plate Elements In order to realize one of the goals of this conversion (that of maintaining a smaller core), something other than a direct replacement with the 18 plate per element LEU fuel had to be pursued. Two basic options lay open: increasing the amount of LEU in some of the plates in an element, or increasing the number of plates in each element. This latter approach was opted for after 1
..:a
' ~
l
- i- ,
La u'8" 38 ;
y the manufacturers announced that they would not make j; 1 available' fuel plates with a higher LEU loading. Since the l
t-Europeans were using elements with 24 plates each, it was determined that it might be feasible to add to the' number of 1 4. plates in the-elements for the UVAR [4]. ANL suggested that :
23 plates per element was the most that should be attempted, so for primarily symmetry reasons (wanting to maintain an l even number of plates), a 22 plate per element configuration t 4 l
was chosen for study.
l - a.
11 In the early stages of this study, a 20 plate per ,
I element configuration was also studied to see if it might be a viable alternative to the 18 or 22 plate options. This option was subsequently dropped in favor of the 22 plate per element option with the reasoning that with more plates in g ,
the element, the element would have a longer lifetime. ,
Longer element lifetime preserves the experimentally desirable more compact core, while also requiring a lesser
' number of elements for a set time period. This latter reason is an economics one which should appeal to the i '
Department of Energy, who pays the fuel bill.
The models for the 22 plate per element cell were a' similar to those using 18 plates. The only difference as far as the codes were concerned between the 18 an 22 plate elements was that in increasing the number of plates, the 1 - . _ _ . _ ._ _
I J
- 39 amount of water between the plates was decreased. This ;
' difference manifested itself only in the IEOPARD models, ;
since it affected the pitch of the plates and the water to '
3 aluminum ratio in the extra (non-lattice) region. Since it
- i. was not known exactly how the plates and moderator would be divided about the control rod in the control elementr., the l
2DB call remained divided the same way as it had been for the 18 plate case. This lack of exactness is irrelevant f a
once the control cell is placed in the core model along with standard cells. ;
L 8 2.2.5 Results The attainable results for these models ,.
include the k.re (or 4 Ak/k, where this is equal to (k.re-l ' ' ' .. 1)/k.cr
- 100) for the case of no control rods, the delta k (rods in to rods out cases) using control rods, the worths I
4 of the control rods, and the radial peaking factors for the ,
g rodded and unrodded cases. 120 rodded cores were not calculated in this section of this project, t'hus these I results will not be given here. Radial peaking factors were determined for some of tha cases run, however since l'
determination of these was not an objective of this part of the study, they shall not be presented here. The unrodded i
k.cr values'and plots will be presented for both the 18 and !
's 22 plate per element core models.
5, A -
m -
- 40
]
3.3 OSTAINING CORE LIFE CALCULETIONS r- e:
3.3.1 Methods of Burnup Throughout the life of the UVAR, attempts were made to build cores in which each of the elements had been burned to approximately the same degree.
Weight factors were assigned to each of the positions in the
- = These factors, when combined with the records of how core.
long and when each element was actually in the core, were used to determine the burnup of each element. None of this was very exact since the weighting factors were only
. estimated and the cores were actually built and added on to l
4 until a reasonable excess reactivity was obtained using the elements available. ,
The best approximate method of calculating the burnup history of the UVAR up to this time may be referred to as a
., perfectly (uniformly) shuffled burn. In this method, the elements are shuffled such that they all have the same i-' burnup at the start of a time step. This shuffle is
. externally forced on the system rather than allowing 2DB to t
do the shuffle itself. Using this method, 2DB is run for each time step, and each run is totally independent of all of the others.
.I;
. A .'
A second method used for calculating core lifetime did 4- not utilize any shuffling at all. This method used the q ,
s ,..
t It .
41 -
capabilities within 2DB.to determine depletion and burnup.
Although no effort was made to approximate the actual burnup patterns of the UVAR usinJ this method, it was done so that
]
a more accurate idea could be obtained of how the HEU' fuel t compared with the LEU-18 and LEU-22 elements.
a
' 2,3.3 Depletion crose sections The first step in doing i depletion calculations was to determine how many time steps !
r 1 l were desired and how big each of these steps should be. The rationale for the limits that were actually chosen shall be 3
(. presented below. Once the desired time steps were 6 determined, this information was entered into the LEOPARD input deck as per the LEOPARD input manual instructions.
ll.' LEOPARD calculated cross sections for each time step, and at '
the and of each, reported the time that had passed and the
, 4-amount of burnup that had occurred by the time of that step.
g The amount of burnup was given in three forms, megawatt days per metric ton uranium (MWD /MTU), percent of uranium burned, ;
I and percent uranium-235 burned. Since the primary idea at t, this point was to compare the lifetimes of the HEU, LEU-18, o
l and LEU-22 fueled cores, when depletion was plotted over 1:
time, the burnup amount in MWD /MTU hhd to be used due to the L
i differing amounts of uranium present from the outset of the a core life. (Note that this was only important for the perfectly shuffled cores as will be explained further in 3'
l section 2.3.4.)
1
- l. i1 42 Once cross sections were calculated for each desired depletion step, they were transferred to bDB via LINX. ;
Methods for using LINX for the transfer of cross sections I which were not depletion oriented were not found. When i.
calculations of an undepleted core were desired, a small ,
5 number of time steps was designated and a run of 2DB was
' os made using the method of perfectly shuffled burn for the-i single (initial) time step. When approached from this 1
manner, the LINX program could be used to transfer cross
'E sections to 2DB. A second means for attaining the same end
, is discussed in.the following.section.
I 2.3.3 Control Region Cross Sections At this time it is t important to point out that only the fueled regions and i their non-lattice regions were permitted to deplete, i.e.,
the cross sections for the control water remained constant I g throughout the life of the core. This policy was followed since burnup cross sections were not attainable for the I control rods as obtained by Wasserman and Freeman, and thus it would have been inconsistent to use burned values for the
'I contr11 water and not for the control rods. It was for this reason that the control region cross sections were chosen to i
be " card read cross sections" as discussad in section 2.1.7, Ig. as this was the only means of permitting the rest of the core to burn while the control rod region (non-lattice 8- region 3 in Figure 2) remained unchanged over time.
4 .. - - _ _ _ _-
g ,
}i
' 43 i
j 2.3.4 calculation of Uniformly shuffled Depletion The uniform shuffle technique relies entirely on the LEOPARD generated cross sections for its depletion. For this method I
a separate 2DB run was made for each time step desired, and each run differed only.in the initial amount of burnup i entered in the input deck. (This value was that MWD /MTU l '! value discussed previously.) One of the options within 2DB l is a choice of what type of search and output is desired.
L For core life calculations, the desired calculation was a l- :
determination of k.cr for the given set of input parameters and situation. Therefore, at the and of each run the 8 corresponding calculated k.tr was given. This value was L
tabulated for each burnup step and for each type of core, and then plotted over time to allow comparicon of the cores.
(These plots are presented later along with the other l' 1 .,
results of this study.)
4 When determining the size of time step to take for this L '
burnup method, a bit of foresight was called for. The goal was to compare plots of k.cr over time for the three types of cores (HEU, LEU-18, and LEU-22), thus each time step chosen I: could represent a point on the plot. Since the core lifetime (for a fixed size core) is determined by how long it can remain critical (k.cr>1) , it was this limit that was used to determine how long the core was permitted to burn.
e i
I ti 44 l Additional output that was requested from the 2DB runs -
.I l was a mapping of the (thermal and epithermal) flux values )
throughout the core. Comparison of two dimensional plots of this data for the differelt cores over time would indicate k
' t; how the flux and power levels changed. Another useful bit of'information from this data was the determination of the
'I' radial peaking factor for each core.
I f, 2.3.5 Calculation'of Unshuffled Depletion The method of ;
,. unshuffled depletion relies on a combination of LEOPARD and 2DB for depletion calculations. As with the uniformly I. 1 shuffled deplation method, LEOPARD calculates depletion cross sections. That however is uhere the similarities end.
For this method 2DB relies on the number and size of time steps put in its input deck, as well as the initial amount 2
- 1. .
of burnup present at the start of the run. One run will '
q- generate calculations for each burnup step requested in the input deck. The only restriction is that since 2DB gets the 1
required cross section values from LEOPARD (interpolating for values that were not specifically calculated), the t values generated in LEOPARD must be able to support the complete depletion requirements of 2DB. The primary requirement is that enough values be calculated to cover th-
.I amount of depletion time over the entire core in 2DB. A practice followed in this study, while not requ'i red, but
'I which allowed for less error in interpolation, was to make r
I,
l}
- 45 the time steps within LEOPARD very similar in size to those I
requested by 2DB.
This practice also came-in handy when the !
1 I f .two~ depletion methods were compared (for this purpose, the depletion steps in 2DB were made identical to those in the i perfectly shuffled depletion steps of LEOPARD) .
I' As with the uniformly shuffled model, cross sections
.were transferred via LINX (with the exception of the afore v
mentioned " card read cross sections"), and similar 2DB I-4 output was requested. Also, tables and plots of k.tr over time-were made and these in turn were compared with each ;
I' other as well as with corresponding data from the other depletion method.
t 1
2.4 CALCULATIONS FOR INCREASED CORE SIEES Ig.
All of the core models described up to this point have been cores that are four elements wide by four elements long I (4 x 4). Since UVAR cores tend to grow in size as they are
~
depleted up to and beyond a 5 x 5 core, these larger cores
~'
needed to be considered in following core lifetimes. Two basic larger core designs were made, these were a 4 x 5 model and a 5 x 5 model. It is important to note that while the 4 x 4 core model was based on the original Texas A & M -
design of 1975, the larger core designs are not based on any I 8 particular former core configuration, rather, they are sort I
l
ju I
4 lI 46 -
of idealized' cores generated o;,1y for the purpose of these i
comparison calculations.
- i i
' s.4.1 4 x s core Model The 4 x 5 core model (Figure 1 12) is a basic takeoff from the 4 x 4 core model; it'was generated by modifying the existing'4 x 4 model in' LEOPARD
, and in 2DB. In LEOPARD, the modifications were limited to the new total buckling value, a larger value for the active
(- '
volume of the element, and a lower power per element factor.
I;j-
- These latter two values are used when the code calculates 1
depletion.
The modifications in 2DB were a good bit more detailed.
l In the model of the core itself, a row of graphite had to be i
l removed so that the new row of elements could be added.
l- . .d .
- l. (Since there are only a given number of positions on the
.g grid plate in the core, and each of these positions is considered to be occupied by either elements or graphite in the models, in order to add something, something else must
- be removed.) Also, to maintain the three cell amount of l reflector surrounding the core in the model, an extra row of l' I reflector water had to be added to the core model.
l- The dimensions, mesh numbers, and region number designations all had to be modified to generate the larger S
core model from the basic 4 x 4 model. Cross sections and 4 . _ _ - __ _ _. - - .
h'i
- s I- 47 I amsm:
g .
.A g
i, 3 g
- 1. .. i g_. i l .
l' GRAPHITE h WATER Figure 12. 4x5 Core Model.
q burnup data-(for the uniformly shuffled cores) were also in !
l need of modification for the new core size. (These values ;
'g needed to be modified since the increased core size affected j the power density in the core, which in turn directly lt I. influenced the burnup calculations for the cross sections.) i 2.4.2 Depletion and Results Burnup calculations were ,
carried out utilizing both of the depletion methods used in I
the smaller core study. As before, plots were made (and I will be presented) indicating the trends of the excess reactivity throughout the life of the core, and core flux I maps were obtained through 2DB output.
1.
^
K.
9 *'.
1 h
48 6
3 .' 4 . 3 5 x 5 Core Model The 5 x 5 core model (Figure
- 13) was developed in the same way'as the 4 x 5 model, with 4-I :
the exception that it used the 4 x 5 model as a base case (as' opposed to the 4 x 4 model). Again, a' row of graphite f
was removed and replaced with a row of standard fuel
'3 elements such that the core was a 5 x 5 array of fueled elements. An additional row of reflector water was added to 4 '
the side from which the graphite was removed to maintain the same thickness of reflector around the core.
s m s . m L s. m (. _
1 l
a _:=
, 3 ::::
$ _EEEEE I
I.3
$ -_ _ "b EE EE 1 g 1
' +
s m m .
m x . w - ms - m m m - s, I
t GRAPHITE @ WATER Figure 13. 5x5 Core Model.
'I, I ._ -_ _ , , , - _ _ _ . - - - , ,, ,
i 49 Modifications to. LEOPARD and 2DB were along a similar-
' 0, r- ~t' 4.? .
vain as those done in creating the 4 x 5 model. All.
- \
depletion calculations were performed and output obtained according to now established routines.
J 1
1 1
i l-I I' -.
p' ri . . g
~ --n- -<=4% .m...+..
I;. t 8
I i l 50
- 3. RESULTS AND DISCUSSION i-.
- 3.1 BENCENARE CALCULATIONS 3.1.1- Basic Data The first thing that had to be done was
- i- to determine exactly what experimental data was available to be matched with the calculations which were to be done. For this information, the records of the Texas 75 core.were 11 looked.at and compared with the types of output able to be 6
L obtained from.the codes. For the neutronics part of the calculations to be done (this project), the only things that could be compared with measured values were the effective I multiplication factors (k.u) with and without the control t . rods. The HEU' calculations could be compared with the LEU calci.ilations, and the basic trends through life could be I
compared with generally expected trends for these types of fuels.
The axial buckling of the various cores was something
! that presented a number of problems. In many of the original runs of 2DB, an axial buckling consistant with what I-was required for the calculational model to match to experimental data was used. The next approxi: nation was a
/
single appropriate value for the core under consideration.
4 This value was about two times as large as the original value used. As will be noted later, this change did not 1 change the lifetime excess reactivity curves, but merely 1 - . . . - - _. _ -- -
')
. , l 51 shifted them upward on the graph. These approximations were necessary since the tools for properly. determining the axial l T buckling (three-dimensional codes) were not directly
.available to UVA at the time. The final approximation used i 3 was' spatially dependent buckling values as obtained from ANL (25-27).
1 ;
W 3.1.2 control Rod Worths The first core to be modeled-1- t ;
and. studied was the first UVAR core having 18 curved a . plates / element fuel elements, the Texas '75. core. The model l-number of this benchmarking core shall be denoted as the HEU-18 (HEU fuel, 18 plates per element) core. The core model is a two-dimensional representation of the active region of the Texas '75 core. ,
The control rods in the model are considered to be either fully inserted, or fully withdrawn. The control rods in the model are independent of I each other'and thus some may be inserted while others remain withdrawn. The next two cores to be calculated also used the model established for the Texas '75 core, however they were done using the LEU fuel (18 and 22 plates / element).
i g .These two core calculations are referred to hereafter as 1<
g.
LEU-18 and LEU-22 respectively. The results of the control rod worths for each of these cases are given below in Table i II.
In the examination and comparison of these and other 1
I
N.
i 52 results, it is important to realize that the experimentally determined values were found using an operating core and not
.j. the idealized situation found with the computer codes.
Thus, the computer model may be accurate even though its
'I results do not exactly match those of experiment.
I 1.
Texas A&M Table II. Control' Rod Worths for the 4 x 4 Jl I Core and Replacements.
- ., - - . s ,. ..a
" Rod"4*t Rod 2* qRod: 3*;-
L l Coreu ':' ~.g' C ; Rod ..1*-
," '($); L($)i l($)V~ .[( $_)f 4
l ,
W; g
},u_)'
l
.'py. 2 ;. /, '
L ;- LTexasM.75j T4;751' "
i5.00 - % f.3;061 : '
( ' 0. 57 '-
ll l(Expt.)? .' ,y.. <
\ ;a- ,
.v. .
3.< . > . ..
? HEU-18; " ~'4.89L, + (2. 79, ~0.71/
l.-
T - 4 . 7 5 '-
<?..'. .
j g.; , *'
- i . . . . ..
- LEU-18 '; ,i "'
l' 1 :.4.73
- 4. 87X
'2.84: 0 .' 7 5 ! ,
l 7: LEU-22
., bl . D. .
f <
l 0.83-
~
K4.79 -
4'.92;,
92 '..96 ~
r s , 7 i
3 ,
i* ENperimAntalfand'ComputationabUncerNdhttiesiareiS%'.(
~
e <s s
s 9 , ,
Ig. The computationally determined rod worths were found by finding the difference in k.tr for each rod between the I inserted case and the removed case. A conversion factor, f 4.rt , was then used to present the worth in dollars. ;
The experimental rod worths were determined using the standard means available (hold three rods in a fixed '
l position and move the fourth). The total worths of the q
~ .
.53 '
I, . three shim rods (containing boron) were all predicted by the t.
l codes to within the experimental accuracy of the 1 measurements. Experimental uncertainty is taken to be iSt. 1 One source of this uncertainty is considered to be the I inaccuracies involved in the measurement of the period.
Another source of uncertainty is introduced when the l'
conversion factor beta-effective is used to determine the I
g worth in dollars. A value of 4.ct= 0.0000 was used since ,
this was the value typically used at the UVAR at the time of operation of the Texas '75 core.
I' The table above also indicates that the control rods will be worth approximately the.same with the LEU fuel as ;
l they have been with the HEU fuel.
3.1.3 Beginning of Life k,cf A second viable 4 il comparison (between the HEU-18 computer core model and the I actual Texas '75 core) was the k.cz value in the xenon-free L. ' l beginning of life (BOL) core situation. Table III below ;
reports these findings for an unrodded (all rods removed) core configuration. The calculated values were taken
. [ directly from the 2DB output information, while the value
' reported for the experimental case could not be directly I determined. (To deter. tine the value directly, the core would have had to be operated with all rods fully withdrawn, whi.h i. - .11 - b1. f.r . , r.. . ., I....... . . . . ..
l _ _
. - - . . _ . , _ . . . _ . ~ _ _ , _ .
.t l
y 54
$ reactivity for the unrodded core'was determined by entering h:. a the critical rod positions into the measured integral rod
{ worth curves.
Table III. Beginning of life Unrodded k.cr for 4' x 4 Texas A&M Core and Replacements.
- h. i - -
?
.u : a as .
DESCRIPTION / ,
8
! B , ' f ';;';w~ ' '
- kJg; ' i L.M q
c .
- Experimental *)'
- n
.g < +"' n.
.. ; r; ;1. 03 611'LO . 005 '
~
L- , ,
g.
~ ,
. ~ z
- ~^w
^ * '
5
' !2DB : Calculations **5 <
... I , l .% '? '4 ' ~
(' ,
( t...'V HEU-18:
- 0.'0017L 3., 'i1.062L . l ryg ' ,
J. ' _ . _
'; g - , '
r p , , D LEU-18t' - -
i- '-0;00181
- g - .;.g
- lQ; ~ ,1140391'c >y.
W- ,
{. , . . . . . . m. ..
W'
- t. ; LEU-22] ,
'O.0018: . 1,2051'l. . .
ze m
.. , ~'
,f$ '
.,, t y' g
[li 8
t ,
8 e ._.I c , , . t> >
. .. . . 4 ~A. .m ,
o.-
'i.
5, I J.
[p* Imp [iedl from.1 Control:-' Rod' Worth! Curvesi..
, a ,
3
.**!All; calculation'models use?an.'extrapolationf, length">
v ':, ot 7 . 8 ' cm . ' ' w . ; ; &.
s i
),
's .* , cy : . .i.
~
x
.. ......i.,......... . . . . . . . . . . . .
I 1
The axial buckling value used in the determination of the calculated ker e was that from the second approximation as described above. This value (indicated in the table above i- as B8 ) is considered to be fairly accurate (for a single buckling value) and is consistent with that obtained by ANL l ~'
_( 4), Meem (18), and an RZ model of the core.
A difference of about 0.02 is seen between the values for k,c for the calculated and the experimental cores. This
j t ,
r I;-
difference may well be due to the problems inherent in' )
1 trying to compara a three-dimensional system with a two- -l
! dimensional model of that three-dimensional system. One of f these problems lies with the fact that the actual critical positions of the rods cannot be taken into account in the
- . model, so while good relative results may be obtained.from- .l J
.the'model (the rod worths), actual values for the core as a 1
y whole may not be so easily compared. A possible reason for this is that since some of the rods must be in the core A while the integral rod worth curves are being generated, a ,
tilting et these curves toward the bottom of the core may
,_"'. result. Itis tilt would then indicate a lower than actual value for the experimental k.tr. This is seen in Table III.
This theory will be tested with a three-dimensional model of lI
- j. the core at a later time. ;
I 3.2 4x4 CALCULATIONAL RESULTS Figure 14 below presents the results of the calculated i
4 x 4 core models over core life using an unshuffled core
.I throughout the core life, and allowing 2DB to perform the depletion calculations. End of core life is defined here as ;
i the point in time at which the core fails to remain critical (k.cr > 1). It should be noted that in reality, the core l will not be considered to be operational for this amount of time since a core must have some excess reactivity in order L to operate successfully. (Excess reactivity is taken to be 1 - _ _ _ . ._ - - _
~ ,
'i I 1 56 I,, the difference between the calculated value of k.cr and the critical value of 1.) The Figure plots excess reactivity i (in % ak/k) versus burnup (in megawatt days (MWD)) . This is t
- a standard means of expressing such information.
% ak/k vs. DEPLETION ,
j 4 x 4 245 i O
-I 5- ,
I.
I l-E 5
M a-I 1 l 2- ,
51 .
[ 1 .-
6 0- ~
m n ~,
3 -1 , , , , , , , , , , , , ,
l' 0 40 80 120 160 200 240 280 u O PEU + U e o LEU 22 i ,
i Figure 14. Reactivity of 4 x 4 Cores Over Time 1'_1 l' From the graph, it is seen that for a 4 x 4 core model,
- 1. ,
the LEU-18 core has a much shorter life than does the HEU core, while the LEU-22 is seen to have a slightly longer l :
ll life than its HEU counterpart. Since traditionally, the 1
- i. UVAR has been operated starting with a 4 x 4 core arrangement and allowing the core size to expand as the core 4
burns, this plot indicates that for an LEU-18 core, such an I.. . .._ _ __.__.. _ ._ ___ __.._._ _._, , . _ _ _ . _ _ . _ . . . . . . _ _
.,..._a u , ,
t
- 57 L
option would not be practical, and a bigger core might have J to be used at the start.
3.3 4E5 CALCUL&TIONAL RESULTS 3.3.1 _ Depletion Methods There were originally two methods of depletion used for part of this study. Both l
methods were applied to each of the different core sizes; however, since the results of these methods for each core size were comparable between the core sizes, only the i comparison for the 4 x 5 model will be presented here.
. Figures 15 and 16 compare the two burnup methods quite well.
/ In doing the calculations to obtain these Figures, the acdels were identical in every way except those that i
_ pertained directly to the depletion calculation itself.
1-It should be noted that these figures are presented l
L only to illustrate the difference between the depletion methods. Many modifications were made to the models after j,
these graphs were generated and therefore they should not be q
accepted as final results. Some of the modifications include: upgrading the axial buckling to the second and 4: finally the third approximations, changing the fuel meat from U3 Sia to U Sin-Al to include the small amount of Al used as the " glue" for the U3 Sin powder, and modifying the boron equivalent content of the altuninum in the elements.
1
, y ~
l 5.
s 58 s
% ok/k vs. OEPLETION
_._.-.m..,_
I 4-
?,
E t 3 h'
3 I -
i
[
0 , ,
- 9 , , . . . . .
0 0 to 120 10 900 Dec 950 maw tav>
a u . u4 . uu en
. . Figure 15. Reactivity over Time for 4 x 5 Uniformly Shuffled Cores.
% ok/k vs. DEPLETION
_.0..._
t ,
s, p
n i s-h I ,,
R I. ,.
- n -
0 a a m 2.o = O m N (W e , . uu se . uu s:
Figure 16. Reactivity Over Time for 4 x 5 Unshuffled cores.
i
- . . . ._-_m.._.__
e f '
59 The figures clearly indicate that the uniform shuffling practice attempted for the UVAR.was counterproductive. The unshuffled cores in Figure 16 tended to last up to 50%
longer than their " perfectly shuffled" counterparts of u Figure 15 because of a certain amount of natural power 7
flattening. Having demonstrated that these results held true for each different core size as well as for cores with many different modifications, it was decided to recommend that the idea of the uniformly shuffled core be abandoned.
l' s 6
3.3.2- Axial Buckling Trials As discussed above, three I
approximations have been made for axial buckling. A
> comparison of the effects of each on the 4 x 5 core model is l' made here. The figures below illustrate this comparison.
Figure 17 uses the first approximation for buckling, with an extrapolation length, d = 4.5 cm. This graph is the same as 4
Figure 16 above, and thus several modifications were made after this graph was obtained. Figure 18 uses the second approximation for the buckling, with d = 7.8 cm. All modifications previously discussed (appearing immediately before Figure 15) had been made at the time of the
., . generation of this graph. Figure 19 is considered to be the most up-to-date representation of the core calculations done
,~ at UVA up to this writing. This graph uses the third approximation tor buckling (spatially dependent), and is in all other respects identical (computationally) to Figure 18.
jt :
- j lI 60 l t.ue vs. ocptti:0N I
,, ,g, l
,I l
' = ~ ~ ~
e
. . . . , )
i i
I j.
'l g
.< (y ,
l :: 1 ::
B l
( .
!i ",,,,,,, .. . T." . . .
g Figure 17. Reactivity Over Figure 14. Reactivity Over Time for 4 x 5 Cores Using Time for 4 x 5 Cores Using ,
1st Buckling Approximation. 2nd Buckling Approximation. .
!I i
i n6Ut vs. OEPLEflCN n eut vs. DEPLETION f l _
3 :: :: l
,g 4
,:x..
(
I :( >
I l ::
'N
.N N I ::
%\ !
l l l- 't._ ,,
. . a e . a a a i S. .. . T.* . . . .. . T.* . . . (
'i
,l Figure 19. Reactivity Over Figure 20. Reactivity Over iW Tile for 4 at 5 Cores Using Time for 4 x 5 Cores as ,
1- 3rd Buckling Approximation. Calculated by ANL.
t -
l
( 61 The final graph, Figure 20, represents calculations done by ANL (27) of the 4 x 5 UVAR core. ANL has independently calculated each of the 4 x 5 cases using both a three-dimensional model and a two-dimensional model with appropriate spatial axial buckling values. These two models reported similar results upon comparison. This graph was generated using the three-dimensional analysis of the core in seven energy groups. (computations done at UVA were done using a two-dimensional core with only two energy groups.)
i General examination (due to modifications made between Figures 17 and 18) indicates that the change to the second i
axial buckling approximation (from the first approximation) tended to lengthen the lives of the core by a factor of about two. The change then to the spatially dependent dxial buckling induced very little change to the curves, though she slopes are seen to change a small amount. Comparing Figures 19 and 20 indicates that UVA and ANL predict the HEU cores essentially identically, while for the LEU curves UVA L predicts % Ak/k values that are consistently about 1% lower than those predicted by ANL. Reasons for this small
\
discrepancy seem to be based on differences in description of the LEU meat (UVA uses U-235, U-238, U-234, and U-236 per Table I while ANL lumps all uranium which is not U-235 I togethe:: as U-238). UVA also considers the extra water on
'- the outer sides of the two end fuel plates to be part of the I
o
s f 62
- non-lattice region (see Figures 6, 7, and 8), while ANL increases the amount of water between each fuel plate to make up the difference.
t Referring specifically to Figure 19, it is seen that the HEU and the LEU-18 cores had approximately the same length of core life, while the LEU-22 core has about a 50%
longer life. This was to be expected, since the LEU fuel 1
(when using 18 plates per element) was designed to be an approximate replacement for the HEU fuel for a standard 18 plate element. Therefors, the confirmation of similar i lifetimes for the HEU-18 and LEU-18 cores was another verification of the methods used by UVA in this study.
3.4 8 m 5 CALCULATIONAL RESULTS Figure 21 below illustrates the effects of the I different fuel element types on core life. From this graph, it is seen that (as was true for the 4 x 5 case) the MEU-18 I and the LEU-18 have similar lifetimes, assuming no shuffling is done. In addition, the graph indicates that the LEU-22 core gives approximately an additional 50% longer life for the core than either the HEU-18 or the LEU-18 cores, at a
, ...t .f 20% ..r. f. 1.
t L 63 4
% ak/k vs. DEPLETION s6 s cens se Ji 39 l So m
\ ..
e ,-
t o-3 4
g
{
i o o: o'. o's o'o 3:e 3.4 o .ev e&YZ5
. teu se e teu ::
i Figure 21. Reactivity of 5 x 5 Cores Over Time.
3.! ADDITIONAL REU TO LEU COMPARISONS Referring to Figures 23, 24, and 25 below, it should be noted that in all cases, as well as for all core sizes, the
[ HEU core starts out with a higher kett than do its LEU counterparts. This is because the LEU cores have a harder f
neutron spectrum and tend to rely more on neutrons leaked back into the core more than the HEU core does. This was expected, and can be seen in Figure 22 below. At the core-reflector boundary of the thermal flux traverse, a much steeper slope is seen for the LEU-22 case, while the least i
l
s 64 steep slope is seen for the HEU case. A negative slope (as seen in this Figure) indicates that neutrons are leaked into the core, while a positive slope would indicate that neutrons are leaking out of the core.
FIux Traverse for BOL in a strection 1
3.5 -
S. t
,g, ,
b V
0.5 -
W G F C F G w 0 '
0 b eD b o mv . T5"' e au n w w.i., e o , . ,n ii . r ro.i e conic.i w.i.,
Figure 22. Thermal Flux Traverse in the Direction Through the Fuel Plates and Through the Peak Flux Value in the Fueled Region.
It should be noted that changing the boundary will affect I
the leakage of the neutrons (exchanging graphite for water I
would decrease the slope, thus indicating that fewer I
neutrons are leaking into the core, or even that the neutrons are now primarily leaking out of the core).
I
'Il' 65 l
I It also should noted (from Figures 23, 24, and 25) that I i the burnup curves for LEU are less steep than are those for
,I j HEU. Thus, as the cores are depleted, the LEU cores (18 and j 22 plates / element) tend to have larger amounts of excess c reactivity than the HEU-18 cores. This cross-over occurs at !
different times in the core life as determined by the core I
size and number of plates. In the case of the 4 x 4 cores, {
the cross-over never occurs for the LEU-18 core, while it i
k i occurs at about the halfway point in the life of the LEU-22
- core. For the case of the 4 x 5 cores, the HEU and LEU-18 ;
cores do not c :
r l
4 ok/k vs. DEPLETION ;
. . . cones so -
l, :
lg ; *- l l5 3 >- i iI i *m l j
l l
g l .-
l e - !
l
- g ; N% i i ,
3, o .eu . Ye* . teu re i
I E Figure 23. Reactivity of 4 x 4 Cores Scaled to the Life Time of 4 x 5 Cores, i 9 . _
I 66 meet until somewhere near the end of life (exactly where is still being debated, however UVA's best guess puts it a bit beyond the end of life). The LEU-22 crosses over the HEU very early in its life at about one fourth of the LEU-22
- core life, thus it has about a 50% longer life than the HEU core.
% Ak/k vs. DEPLETION io -
, .s 7
B 3 t-I h s-
$ s.
B E '
\
)
=-
\\
1-B ., I %=
1 ' ' ' '
roo .o ;o .=
o . . O.("*' . av ==
Figure 24. Reactivity of 4 x 5 Cores.
The 5 x 5 cores show a continuation of this trend, with the
(
HEU/ LEU-18 cross-cVer occurring shortly before the end of
- j. core life, and the HEU/ LEU-22 cross-over occurring near the beginning of core life.
8 i
Y
(~ 67 1'
% ak/k vs. DEPLETION
$ a S Comel
{
90 m \
n 9-l 6-
! l-3=
I ,. w ,
0
-i , -. , , , ,
0 200 a00 600 930 km4# (wee o .eu . teu se e teu er i
Figure 25. Reactivity of 5 x 5 Cores Scaled to the Life Time of 4 x 5 Cores.
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4 p
68
- 4. CONCLUSIONS AND RBOOMMENDATIONS
4.1 CONCLUSION
S This study had as its purpose the benchmarking of the l} HEU 18 plate per element 4 x 4 core, the calculational comparison of the HEU-18, LEU-18, and LEU-22 fueled cores for different sized arrays, and the determination of the optimum LEU fueled basic UVAR core. A basic model of the i
benchmark (4 x 4) core was developed and was compared with the experimental results obtained in 1975. The worths of the three control rods were predicted almost exactly, while i the prediction of the far less important stainless steel regulating rod was not quite as accurate. The control rod worths for the LEU fueled cores were also predicted, and it was concluded that the conversion to the LEU fuel will 1.ot, i
significantly change the control rod worths.
I The krr values for each of the unrodded 4 x 4 e
I' calculated cores and for the benchmark core were compared for the beginning of life case. The difference of 2%
)
between the HEU-18 model and the experimentally inferred i
benchmark case indicates a real need for calculations to be I
done using a three-dimensional model so that the effects of L the control rods being partially inserted might be properly included. The comparison of these initial keer values I between the calculated cores showed that there is a fairly 1
4
[ 69 considerable difference between the HEU-18 and the LEU-18 from the very beginning, with the LEU-18 starting out its life with a k,,, 2.3% lower than the HEU-18. The LEU-22 core should start out with about a 14 lower k.tr than the HEU-18.
t From the study of the unrodded 4 x 4 cores, the i conclusion was reached that, given the relatively low initial value of kort followed by the sharp drop in k over a t
very short period of time due to xenon poisoning, the LEU-18 fuel arranged in a 4 x 4 core would have such a relatively short operational life that it is not to be considered an a acceptable option for use in the UVAR.
I 8 Depletion studies were conducted, examining the trends
,, of keer over the course of the life of the core. Based on i
these results, it was determined that the shuffling method g
followed in the past for the UVAR was counterproductive and should be abandoned in favor of no shuffling or some other i improved shuffling pattern.
5 I comparison of k.tr trends over core life for different values of axial buckling (in 2DB) indicates a very strong relationship exists between k and the axial buckling. This is illustrated in the comparison between the first and the second buckling approximations used with the 4 x 5 cores s where the axial buckling was almost doubled in size, and the B
I
[
4 effect on % Ak/k was almost a 2% increase. When the buckling was allowed to vary spatially over the core rather than maintain a single value for the core, essontially no change in 4 Ak/k was noted. This leads to the conclusion that while the spatially dependent buckling may be "more correct", the single value approach used for the axial buckling was quite a good approximation, and may be used when other "better" values are not to be had.
It is well known that a smaller core will produce a higher experimental flux at the same total power than a larger core will, and it is for this reason that UVA would like to be able to maintain cores of the size of a 4 x 5 core for a longer period of time. After studying the excess reactivity trends over core life for the 4 x 5 and 5 x 5 cores (and with the unshuffled and the uniformly shuffled depletion methods), it was found that the LEU-22 fuel in the 4 x 5 core had only a slightly shorter life than did the HEU-18 in the 5 x 5 core with no shuffling used in either case. (It was also found, thougl. not explicitly presented here, that the LEU-22 in the 4 x 5 core (unshuffled) had approximately the same life time as the HEU-18 in the 5 x 5 core using the shuffling methods in practice for the UVAR (uniform shuffling).) Therefore it seems to be strongly to the benefit of the UVAR experimenters that the LEU-22 fuel be adopted so that a smaller core size might be maintained E
- - - - - - --~ .
I l' 71 i
![
W for a longer period of time.
I The LEU-22 fuel not only has a longer life than the
{
HEU-18 fuel does, but it maintains a higher level of excess i reactivity for a longer period.of time. This converts to a smaller amount of change in the core over time for the LEU-22 fueled core. Traditionally, since various parameters of f the core (control rod worths) must be recalibrated as time [
t 1 goes by due to such changes in the core, a core that changes
- g. less over time would be very desirable since it hopefully would not require recalibration as often. Another benefit I of the slower changing core would be that the fuel elements ;
- would not have to be shuffled as often to maintain a " good" l Core. >
t i -
i- For the case of the 4 x 5 core, the LEU-22 fuel was l l predicted to give about a 50% longer core life than the LEU-18 would be able to give. This increased core life is
- especially impressive when it is considered that a 50% !
increase is obtained for only an increase of 20% more fuel.
l.
From this it is seen that adoption of the LEU-22 fuel would ;
require a slightly higher initial expense per fuel element ;
g on the part of DOE for the purchase of the new fuel,. but
)I this would be more than repaid by the fewer number of fuel
. elements that would have to be purchased, and in the fewer ;
4 number of used fuel shipments that would have to be made.
1~ --
g-72 The final comment to be made is that while all of these calculations were done at WA, and all of these conclusions were reached as a result of work done there, the 4 x 5 WAR core was also calculated at ANL. A comparison of the j
results shows that the calculations done at WA using the tools and computer codes available, are quite acceptable.
I 4.3 RECOWLENDATIONS The recommendation made based on these studies is that the University of Virginia should adopt 22 plates per i
elemert LEU fuel rather than the 18 plate per element standard. A relatively small initial higher fuel 4
fabrication cost is incurred (production costs for the i .
structure of the element and the individual plates remain the same, however more plates means more cost per element),
t but the use of the LEU-22 fuel easily offsets the cost of replacing all of the elements at a much earlier time than I would be required for the LEU-22 core, and leads to a cost savings in the end.
A second recommendation to the WAR facility itself would be to abandon the shuffling pattern used thus far for the WAR, and adopt a more beneficial one. To this end, ANL has recor. mended the adoption of an equilibrium-cycle shuffling pattern based on the adoption of a fixed 4 x 5 l
q..
4, 73 core. This shuffling pattern, while potentially being a great boon to the facility, should not be permitted to limit core size and configuration as the experimental need arises.
4 I
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l' 74
- 5. FUTURE WORK ON TEIS PROJBCT This part of the HEU to LEU fuel conversion effort was concerned primarily with the determination of the appropriate methods with which to proceed with more in-depth studies for the UVAR. Several of these studies were mentioned previously; however, to complete the calculations required for NRC licensing approval, many more studies are required.
All calculations presented here for the LEU fuel were done based on modifications to the Texas A&M fuel elements.
Very simply stated, the LEU-18 elements were treated as if the fuel plates were removed from the HEU elements and replaced with LEU fueled plates. The LEU-22 elements were treated by taking eighteen times the pitch of a single LEU-l 18 plate / moderator section and dividing it equally twenty-two ways. This was done since at the time no better l information was available as to the actual elaissil, configuration. As " official" LEU element drawings become available, the LEOPARD and 2DB cells will have to be modified accordingly. The changes to be made are very slight and should only affect the water gap between the plates. The new elements will be designed such that (for the case of the UVAR) 18 (or 22) times the pitch of a fuol plate will be equal to the width of the element as dictated
75 by the grid plate. This is made possible when the plates in the element are flat rather than curved as they are for the HEU fuel in the UVAR.
I Since, based on this study, UVA will only be actively interested in the 4 x 5 core array fueled with the LEU-22 fuel, this is the only case that need be studied in more depth. The studies should take into consideration the range of core boundaries that have been used, are planned to be used, or are even as yet unplanned conditions. Some of these boundaries would includes permanent experimental i facilities on one and two faces of the cere; open bean ports li on one, two, and three sides of the core; and the addition of a Dao tank on one face of the core.
I -
II other boundary changes that need to be studied involve i
t specifically the reflector region of the core. For the
' calculations done in this study, the maximum amount of I graphite allowed by the grid plate was used. As evidenced by the high excess reactivities calculated under these i
conditions, these were not "true to life cores". Graphite should be removed and replaced by water in various arrangements around the core.
41 Finally, the positions of the control rod elements are not fixed and may be moved if it is considered beneficial to
{I
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4 L' 76 do so, thus it is important to determine the effects computationally of several possible control rod contigurations.
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77 APPENDIE The Figures 26 and 27 illustrate, to some extent, the variety of core configurations that have been used in the UVAR in the past several years.
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@ WATER Figure 26. Long Core Experiment.
.. .=....-...- . . ~ . .
{
78 i e
- l EXPERIMENT l 3 I
s !
t ,
g -,L !
e :
6 .: ,
5 -
2
[
1
- S _
R h 1
i,
? !!! RB s
a l
I, - t gg GRAPHITE s SOURCE '
1
! I' R. RB RADIATION 1
WATER FACILITY ;
\ >
{
Figure 27. Sample EPRI Core. f i ;
1 l
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j . _ _. . . _ . _ _ . _ ,
l' II 79 The Figure 28 illustrates the current appearance of the reactor core, the reactor pool, and some of the surrounding I
e facility.
r
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g - ,
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- O N
t
- i e i rigure at. Ground Floor View of Reactor Face, Pool, and Approximate Position of l-
- Core. .
1 q
'i Ii __ . . - . . . . _ . . _ . _ . . - _ . _ _ . . _ _ . _ _ _ . _ . . _ _ _ _ . _ .
o ]
,t-s 80 i REFERENCES (1) " Limitations on the Use of Highly Enriched Uranium (HEU) in Domestic Non-power Reactors," 10 CFR !
> 50.64, Jan. 1, 1987 Ed. !
l
[2] " University Plate-type Reactors LEU Fuel Options,"
copied page sent to all project participants by ANL.
i' (3) Meeting of all university participants in 1
,3 conysrsion project. RERTR atg. at ANL, July, 1987.
(4) Private communications with J. Matos (ANL) j throughout project's duration.
I "MTR Fuel Shipped to University of Virginia on 10-(5) '
23-73," document on file with UVAR reactor Administrator. ,
t l (6) " Fuel Element - Standard," bluenrint # NE-33. i Nuclear Science Center; A&M College of Texas, ;
l Department 7f Nuclear Engineering, Sept. 6, 1960. l, l
(7) " Fuel Element - Control Rod," bluenrint # NE-34. l l Nuclear Science Center; A&M College of Texas, +
4 Department of Nuclear Engineering, Sept. 6, 1960. -
l
[8] " Modified Reflector Element," bluenrict # UVAR 1222, University of Virginia Reactor Facility.
[9] " University of Virginia Test Research and Training !
Reactor 2 - Fuel Plate," bluenrint # 409337. EG&G Idaho. Inc., Aug. 5, 1980.
i (10) " University of Virginia Test Research and Training i Reactor 2 - Standard Fuel Element Assembly,"
bluenrint i 409338. EG&G Idaho. Inc., Aug. 8, 1 1980.
A (11) " University of Virginia Test Research and Training Reactor 2 - Control Fuel Element Assembly," !
bluenrint # 409339. EG&G Idaho. Inc., Aug. 6, i' 1980.
)
l (12) " LEOPARD Manual," (summary of the LEOPARD input description contained in WCAP-3269-26, Sept.
1963.), May 29, 1981.
1 - _ _ _ _ _ . __
S' l'
e
~
81 s
(13) Wasserman, S., MS thesis, University of Virginia, 1989, in process.
N.
(14) "QA Package for Control Rod Worth, Shutdown Margin, and Excess Reactivity Study," D. Freeman, August 1988.
4
' (15) "2DBUM," finnut manual for 2nnUM. Version a 6.
5/9/80).
(16) "2DBUM ( APOLIA VERSION) ," fineut manual for 2DnUM.
> Version # 10. JULY 86), Sept. 1986.
I (17) " Dimensions of the Grid Plate," Memorandum.
I University of Virainia Denartment of Nuclear Enaineerina and Encinaarina Physics. Reactor
'n Facility, (tot The LEU Conversion Participants),
B. Hosticka, Apr. 29, 1988.
l (18) Meem, J. L., Two Groue Reactor Theory. New York:Gordon and Breach Science Publishers, 1964.
(19) Personal Correspondence from ANL (Woodruff),
reflector water cross sections.
(20) Personal Correspondence from ANL (Woodruff),
reflector graphite cross sections.
[21) " Specification for Test Research Training Reactor i 120 Silicide U3 Si2 Fuel Plates," TRTR - 5, EG&G Idaho, Inc., Rev. 3. Apr. 5 1988.
(22) " Specification for Low Enriched U Metal for Reactor Fuel Plates," TRTR - 11, EG&G Idaho, Inc.,
Rev. 1. Apr.1, 1987.
[23) " Specification for Reactor Grade Uranium Silicide U.Sig Powder," TRTR - 14, EG&G Idaho, Inc., Rev.
- 2. July 1, 1987.
t':, " Specification for Aluminum for Fuel Plate Core Matrix," TRTR - 15, EG&G Idaho, Inc., Rev. 2.
July 1, 1987.
(25) "Regionwise Extrapolation Lengths for UVAR 4X5 HEU Reference Core (ca. ) ," FAX copy frca ANL (Matos) to UVA (Fahr). Sept. 2, 1988.
(26) "Regionwise Extrapolation Lengths for UVAR 4X5 LEU-18 Reference Core (ca.)," FAX copy from ANL 8
(Matos) to UVA (Rydin). Sept. 9, 1988.
l
,_ - _ , _ . . . - . . . - . - . - - - - - - - ~ ~ - - - - - - - - - -
y 82 (27) "Regionwise Extrapolation Lengths for WAR 4X5
[ LEU-22 Reference Core - (ca. ) ," FAX copy from ANL (Matos) to WA (Rydin) . Sept. 13, 1988.
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