ML20212N402

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Difxy,Fortran Code for Solution of Multi-Energy Group Diffusion Equations in X-Y Geometry
ML20212N402
Person / Time
Site: Rensselaer Polytechnic Institute
Issue date: 03/03/1987
From: Harris D
RENSSELAER POLYTECHNIC INSTITUTE, TROY, NY
To:
Shared Package
ML20212N386 List:
References
NUDOCS 8703130008
Download: ML20212N402 (23)
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Text

. _ . __

REFERENCE 5.

DIFXY, A FORTRAN CODE FOR SOLUTION OF THE MULTI-ENERGY GROUP DIFFUSION EQUATIONS IN X-Y GEOMETRY D.R. Harris Rensselaer Polytechnic Institute Troy, New York Abstract DIFXY is a Standard FORTRAN code for solution of the multi-energy group diffusion equations in x y geometry. The difference equations are mesh point centered and in this respect, as well as in the layout of the the _ x y

, geometry, DIFXY conforms with the widely used PDQ codes and yields similar l results. DIFXY operates on a PC, is small, and a dictionary is provided defining all variables. Input and output are in fixed field formats and are identified by variable names. DIFXY carries out eigenvalue problems and l

source problems with or without fission, and forward and adjoint solutions as well as reactivity inner products from the forward and adjoint results. DIFXY depletes according to macroscopic cross sections which are polynomials in burnup; no nuclide chains are provided.

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Introduction ~

Multienergy group diffusion solutions are widely used in reactor analysis. DIFXY solves the multienergy group diffusion equations for any number of energy groups with arbitrary up and down scattering. The difference

- equations are mesh point centered and are in accord with those used in the PDQ codes, .as are the geometry specifications. Iteration and convergence used.in.

DIFXY and PDQ are different, but as these do not. generally affect the results the results are found to agree when both codes are sufficiently converged.

DIFXY solves eigenvalue and source problems, direct and adjoint problems, and it can calculate reactivity worth inner products from the direct and adjoint solutions. Zero flux or zero current boundary conditions are separately l applied to the four outer boundaries; repeating arrays and shuffle are not provided for-in DIFXY. DIFXY depletes according to macroscopic cross sections which are polynomials in burnup; no nuclide chains are provided.

j Program DIFXY is a clearly written Standard . FORTRAN code of less than 500 statement lines. The code has operated on a variety of PCs and mainframes. A dictionary (Appendix A) provides a definition for every variable. Input utilizes only three fixed field formats (20A4, I4, E12.6), and all input is l echoed. Output items are identified by their variable names which are defined l in the Appendix.

I

_The difference equations in DIFXY are those given in Ref. 1, Section 2.4.

DIFXY uses optimized successive overrelaxation (SOR) for convergence of the i

inner iterations, and it has used several techniques for convergence of the outer iterations, including SOR and Chebyshev. Convergence criteria are provided for (a) the maximum relative change in flux in any energy group and at any mesh point (not just the mesh points where there is fission as in PDQ, see Ref.1, Eq (2.2.1)) from iteration to iteration; (b) maximum relative change in fission neutron source at any mesh point; and (c) relative change in multiplicative eigenvalue. Exeprience has shown that convergence for the fission neutron source is least rapid. Further convergence is very rapid after moderate convergence is obtained; thus stringent convergence criteria (10-5 or 10-6) are usually used. The error and convergence situations at each iteration are edited.

j Input All variable names in DIFXY follow the simple FORTRAN requirements on type (variables beginning with I, J, K, L, M, or N are integer); thus the format for a variable (I4 for an integer variable field, E12.5 for a real variable field) can be recognized immediately from the variable names. All input is echoed.

j l

4 3 l The input first requires job data, j Job. Title (Format 20A4)

KE,KP,KXM,KYM,KXP,KYP,KA,KW,KB NXR,NYR,NR,NRC,NM NG,NI,NO,NB,NP EF,EE ES,AI,AO,BS This is followed by geometry data beginning with mesh lines (which must, as in PDQ, go entirely through the geometry layout),

IXR,MXR(IXR),XR(IXR) for IXR=1,NXR IYR,MYR(IYR),YR(IYR) for IYR=1,NYR Here, for command IXR,MXR(IXR) mesh intervals are put into place in the x direction with spacing XR(IXR)/MXR(IR), and similarly for y. The mesh lines bound small rectangular " mesh figures". . A region consists of one or more such mesh figures. All mesh figures are first labeled as region 1, then other region numbers are overlayed intil the desired region distribution is t obtained. A region contains a single material " mix," i.e. , cross sections are

i. the same throughout a region, and tb a mix numbers JM(IR) are next supplied for each region IR, (JM(IR),IR=1,NR) p The region overlay is supplied next. For each of NRC region overlay commands one supplies for each command

( JRC,LX(IRC),MX(IRC),LY(IRC),MY(IRC) for IRC=Q,NRC 4

A particular overlay command assigns region ID numbers JRC to all mesh figures

, between x coordinates LX(IRC) and MX(IRC) and between y coordinates LY(IRC) l and MY(IRC). A sequence of such commands can lay out any required set of I regions. A region map and a mix map are edited for each job (see I

Appendix C).

Finally, the cross sections are input. For each cross section mix (IM-1,NM) the first quantity read in in the transverse buckling (B )2named BZ, in units of cm-2 Then for each energy group (IG=1,NG) are read in the

six index IM, the group index IG, the diffusion coefficient DF(IM,1G), the complete group loss (absorption plus removal) cross section SA(IM,IG), the fission neutron production (v[f) cross section SN(IM,1G), and the fission j energy (c[g) production cross section SE(IM,IG). On one or more subsequent lines is the full outscattering vector (SS(IM,IG,IH),IH-1,NG) for particle I transfer from group IG to IH. All these cross sections are macroscopic and l are input in units of (barn em)-1 for croas sections and em/ barn for diffusion i coefficient. Specifically for each cross section mix IM, the read commands are l

1

4 BZ DO....IG=I,NG READ (5,14) IH,IG,IP,DF(IM,IG),SA(IM,1G),SN(IM,IG),SE(IM,IG)

READ (5,11) (SS(IM,IG,IH),IH=I,NG)

The input indices IM and IG are only temporaries for clarity in visual interpretation of input files; if they are input out of order, however, they are edited with minus signs to alert the user. The same comment applies to the indices IXR and IYR appearing earlier. If burnup is not requested (KB control) then the number of burnup steps (NB) and the burnup per step (BS) need not be input. If burnup is requested then these parameters must be supplied as well as NP other sets of cross section data representing coefficients in polynomials in burnup.

A sample input appear in Appendix B. The corresponding output appears in Appendix C.

Output Core layouts are provided showing region and mix assignments for each mesh figure (see Appendix C). Fluxes, fission neutron sources, and energy production are edited for each mesh point.

Code Testing The DIFKY code has been tested .by comparing its calculations against (a) PDQ-1 calculations, and (b) analytic solutions. The analytic solutions arise when, for a uniform medium, one uses zero current boundary conditions on two opposite outer boundaries and zero flux conditions on the other boundaries. This results in effectively one-dimensional problems with known analytic solutions. DIFXY results for these tests have agreed within the accuracies of convergence.

References

1. C.J. Pfeifer and C.J. Spitz, "PDQ-8 Reference Manual,"

WAPD-TM-1266 (1978).

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l APPENDIX 1 l

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Unchanged Technical Specifications definition of Control Rod Assembly.

New SECTION 4.4 of the Safety Analysis Report.

New SECTION 5.4.4 of the Technical Specifications.

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s- x, TEC10iICAL SPECIFICATIONS DEFINITION OF CONTROL ROD ASSEMBLY: .,,

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Cont'Eo1 Rod Assembly' ' A contiol nachanism consisting "of a stainless steel 9 basket that houses two absorber sections, one above the other. These absorber sections may contain'either enriched borop in iron, Eu03 in a stainless steel cermet, stainless steof; or an alloy of silver-cadmium-indium. All absorber sections except the one containing silver-cadmium-indium are citi in stainless N steel. All are of the ssme. dimensions, nominally 2.6 inches sqhare, with' ,

.their poisons uniformly distributed. The absorbers, when' fully: inserted, shall:' extend above the top and to within one-inch of the bottom of the active l core. , ,

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SECTION'4.4 0F THE SAFETY ANALYSIS REPORT.

4.4 Control Rods.

Four control rods are provided, spaced 90 degrees apart at the. core periphery. Each rod consists of.a 2.75 inch square stainless steel' tube, 65

. inches in length, which passes through the core and rests on a-hydraulic buffer on the bottom ca refer plate of the support structure. Housed in each of these " baskets" are two neutron absorber sections,'one positioned above the-

.other as depicted in Figure 4.8. These absorber sections may contain either enriched Boron (in B10) in iron, Eu03 in a stainless steel cermet, or an alloy.

of silver-cadmium-indium. All-absorber setions except the one containing silver-cadmium-indium are clad in stainless steel. . All absorber sections are of'the same dimensions, nominally 2.6 inches square, with their poisons uniformly distributed.

- The relative worth lof these absorber sections was measured, in an outcore position of the HEU core, by the rod drop method. Results are given as e follows.

Absorber Reactivity Worth [d]

A-1(B10) 27.17 A-2(B10) 23.27 A-5(B10) 22.24 16 (B10) 18.83 MA 22.15 (Eu03 )

L (B10) 16.92

, H (B10) 23.61 i

SS (Stainless 4.99 Steel)

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Absorbers - A-3, A-4, A-6, and A-7 were part of the ' control rods for the. HEU core.. Therefore necessary changes to the absorber section of the control rods to accomodate the larger axial dimension of the LEU. core (36" active length) can be made by using existing absorber sections, n'

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5.4.4 Control Rod' Assemblies Four control rod assemblies are installed, spaced 90 degrees apart at the-core periphery. Each rod consists of a 2.75 inch square stainless steel tube which passes through the core and rests on a hydraulic buffer on the bottom carrier plate of .the support structure. 11oused in each of these " baskets" are two neutron absorber sections, one positioned above the other as depicted in Figure 4.8 of the SAR. The combination of the four rods must meet the Technical Specification,'given in Table 5.2, with regard to reactivity with one stuck rod and shutdown margin.

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'2.1 : Safety Limits - Fuel Pellet Temperature Applicability Applies to. the maximum temperature reached in any core fuel pin pellet due to either normal operation or transient effects.

Objective To identify the _ maximum temperature beyond which material degradation of the fuel and/or its cladding is expected.

Specification Fuel pellet temperature at any point in the core, resulting from normal operation or transient effects, shall be limited to no more than 2000*C.

Basis-Specific determination of . the melting point of the SPERT fuel has not been reported. ' A safety limit of 2000*C is below the listed melting point of UO2 under a wide variety of conditions._ The chosen value is conservative in view of variations that might result due to the presence of small quantities of impurities and the comparatively high vapor pressure of UO2 at elevated. temperatures. The safety limit specified is about 700 degrees below -the measured melting point of UO2 in a helium atmosphere.*

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Reference:

W. A. Duckworth, ed. , " Physical Properties of Uranium Dioxide,"

Uranium Dioxide: Properties and Nuclear Applications (Washington, D.C.: Naval Reactors, Division of Reactor Development), 1961, pp. 173-228.

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-QUESTION 24.

Recently amended Technical Specification 5.6 (to be deleted)

~ Recently amended Technical Specification 5.7 is Proposed Technical Specification 5.6

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5.6 Fuel The fuel used for reactor operation is a plate-type, stainless steel clad, UO2-SS cermet enriched to 93% U-235. Stainless steel clad, SPERT (F-1) - fuel pins, enriched to 4.8% U-235, can be stored in the facility, but not used for reactor operation.

RECENTLY AMENDED TECHNICAL SPECIFICATION 5.7 IS PROPOSED TECHNICAL SPECIFICATION 5.6.

5.7 Fuel Storage and Transfer When not in use, the fuel shall be stored within the storage vault located in the reactor room. The vault shall be closed by a locked door and shall be provided with a criticality monitor near the vault door.

The fuel shall be stored in cadmium clad steel tubes with no more than 1 kg fuel per tube mounted on a steel wall rack. A storage tube in the storage vault can not contain more than 15 SPERT (F-1) fuel pins at any time. The center-to-center spacing of the storage tubes together with the cadmium clad steel tubes assures that the infinite multiplication factor is less than 0.9 when flooded with water.

All fuel transfers shall be conducted under the direction of a licensed senior operator.

Operating personnel shall be familiar with health physics procedures and monitoring techniques and shall monitor the operation with appropriate radiation instrumentation.

For a completely unknown or untested system, fuel loading shall follow the inverse multiplication approach to criticality and, thereaf ter, meet Specification 4.2. Should any interruption of the loading occur (more than four days), all fuel elements except the initial loading step shall be removed from the core in reverse sequence and the operation repeated.

For a known system, up to a quadrant of fuel pins may be removed from the core or a single fuel pin be replaced with another fuel pin only under the following conditions:

1. The net change in reactivity has been previously determined by measurement or calculation to be negative or less than $.72.
2. The reactor is suberitical by at least $2.86 in reactivity.
3. There ir. initially only one vacant position within the active fuel lattice.
4. The nuclear instrumentation is on scale and the dump valve is not bypassed.
5. The critical rod bank position is checked after the operation is complete.

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