ML18043A688

Forwards Axial Power Distributions from Fourier Fitting of Fixed Incore Detector Powers to Clarify Tech Spec Change

ML18043A688
Person / Time
Site:	Palisades
Issue date:	05/17/1979
From:	Hoffman D CONSUMERS ENERGY CO. (FORMERLY CONSUMERS POWER CO.)
To:	Ziemann D Office of Nuclear Reactor Regulation
Shared Package
ML18043A689	List: ML18043A688 ML19282D171
References
NUDOCS 7905230095
Download: ML18043A688 (10)

Text

General Offices: 212 West Michigan Avenue, Jackson, Michigan 49201

• Area Code 517 788-0550 May 17, 1979 Director, Nuclear Reactor Regulation Att Mr Dennis L Ziemann, Chief Operating Reactors Branch No 2 US Nuclear Regulatory Commission Washington, DC 20555 DOCKET 50-255 - LICENSE DPR PALISADES PLANT - TECHNICAL SPECIFICATIONS CHANGE - IN-CORE DETECTORS ADDITIONAL INFORMATION This letter is in response to questions received by telephone from the NRC on our In-Core Detectors Technical Specifications Change.

The Conswners Power Company version of the INCA program is being revised to accommodate five (5) levels of detectors.

This will be performed by Consumers Power Company personnel.

The method used in synthesizing axial power distributions is outlined in the attached paper:

"AXIAL POWER DISTRIBUTIONS FROM FOURIER FITTING OF FIXED IN-CORE DETECTOR POWERS" by Terney, Marks, Williamson and Ober, Combustion Engineering, Inc, 1975.

The report gives the equations involved in the fitting procedure and quotes expected errors.

The extrapolation distance o is computed in the Consumers Power Company INCA code by running the XTG program and finding the value of o that gives the best agreement between a fit based on calculated detector powers and the corresponding 12-node XTG shape for each assembly.

Attached are three figures showing examples of comparisons between computed assembly axial power distributions and the corresponding synthesized distributions based on five computed detector powers.

The graph labeled 14 shows a current typical Palisades power shape with no control rods in the core, while the graphs labeled 20 and 26 are for a case with the group 4 rods inserted halfway.

As shown by 14 and 20, the fitting method works extremely well for balanced and skewed power shapes.

Figure 26 shows that while the fit is not as accurate for an assembly immediately adjacent to a control rod, both the magnitude and position of the power peak are still well represented.

ffieJ~

David P Hoff~

CC JGKeppler, USNRC oc0579-0337a-13

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.e ABSTIL\\CT A rel1:able method is needed.for synlhesi::ing Jlw; dc/ec/or readings 1:nto spatially dependent a;i;ial power shapes with a limited m1m/Jer of fixed in-core 11elllro11 detectors in w1 axial siring. In this paper, the Follrier expansion tech-nique for obtaining axial power dislrilmlions is exam.ineq.

A wide variety of representalive a:cial shapes are studied with four,.fire and six detector systems. The results show all the systems perjorrn well. The use of five deleciors instead of four increases the acwmcy, while the use o.f six detectors git-es lillle further irnwo1*errwn.t over the.fil'e-delector sys/em. With.fice defectors and five Fourier modes, the standard deviation in the error in prediclinr1 the axial peak lo average power ralio is about 0.8%.

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AXIAL POWER DISTRIBUTIONS FROJ\\.~. FO.URIER FITTING OF FIXED.. IN-CORE DETECTOR P.OWERS INTRODUCTION General

• With a limited number of fixed in-core neutron detectors, a reliable method is needed to synthesize the detector readings into spatially dependent power dis-tributions. Combustion Engineering's in-core detector analysis system (INCA) is such a method. n-4 > An integral part of the method is the procedure used to synthesize i.:.:,ial power distributions from the readings of a few detectors in an axial string. In this system, a method based on expanding the axial pQwer distribution in terms of a few axially dependent Fourier modes is used.n-G>

Formulr1fion The lmsir: prorcdure is to assume that. the.'xial power distribulion in an assembly may he represented as the sum of the first N Fourier modes:

N P(z) = L an sin n 11" Bz (1) n=l where P is the power per unit length,

• z is the axial elevation in percent of the core height (H),

an arc the unknown combining C'oefficients, and H

B=H+2o (2)

Note that o is the extrapolation distance, which usually is determined empirically.

The N combining coefficients are obtained by match-ing the power read by each of the N detectors to the integral of Eq (1) over the axial extent of each of the N detectors Z ilop

(

N

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di=f dz L an sin 11 7r Hz Z.hottom n=l

'I (3) i=l,... N where d; is the power read by the jth detector and z/*0 P and z;hottom arc the axial elevations ol" the top and bottom of the i th detectors, respectively.

This can be done for all the detectors in a string, or for subsets. For instance, with four detectors, four modes could be used to match all four detectors simul-taneously. Alternatively, the top three detectors could be matched wit.h-three modes, and the l>oLLorn three detectors wi!.11

!.Im~<~ modes. The actual power di:;Lri-bution would then lie made of Lop and bottom segments fron1 the t.wo fit:-;.

In this study, both the overlapping and continuous schemes were investigated. Also, various arrangements of four, five and six detector strings were examined to determine the best arrangement of each. The study was carried out Ly testing the various systems on a large number of typical PWR axial power shapes generated from one-and three-dimensiunal diffusion theory calculations at different times in life for different conditions.

H.ESULTS lnitial studies were done on a sample of 17 skewed power shapes from a set of 170 typical and highly skewed beginning-of-life (BOL), middle-of-liCe (\\IOL),

and end-of-life (EOL) first cycle one-dimensional shapes. Typical examples of t.lw shapes ar.; given in Fig. 1. The use of four and five equally spaced de-2.4~--~---~-~--~-~-~~--

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0.6 0.7 0.8 0.9 LO FRACTION OF CORE HEIGHT Fig. 1: Represenlafive shapes from one-dimensional analyses tectors with lengths equal to 123 of the core height was investigated. as well as using subsets of three detector readings for the fit.ting. The pseudo detector readings were obtained by integrating the given shapes over the detector lengths. Then the fitting was done and compared to the given* shapes. The boun<lary conditions (o or B) were chosen Lo yield a mean error of near zero in fitting axial peak-to-average power ratios.

Table I gives the results for.these 17 one~dirnensional axial shapes with the best four and five detector ar-rangements. \\Vith four detectors, locating the centers of the segments at 20, 40, 60, and 803 of the core height led to the minimum uucertainty in the fitted axial peak. In the five detector system, the centers were located at 10, 30, 50, 70, and 90% of the core height. Two points arc immediately apparent: One is that using the maximum possible number of modes is bdt.er Llian 1isi11g groups or subsets. For four detectors, using four modes is slightly better than using two sets of three rnu<les, sirniiurly for live'dele1.:tors anci live modes.

TABLE I ERROR ANALYSIS OF THE AXIAL PEAK TO AVERAGE POWER RATIO FOR 1-D AXIAL SHAPES Case 4 detectors centered at 20, 40, 60, 80% of core height 2 sets of 3 modes....................*.......................

1 set of 4 modes.............................................

5 detectors centered at 10, 30, 50, 70, 90% of core height 2 sets of 3 modes............................................

1 set of 5 modes..........*..................................

real -fit

% error= --- X 100 real Further, it is clear that a five detector system is an improvement over the four detectoi* system. The reason for Lhis is twol'old:

(1) With five detectors. Lhc peaks near Llic end of tlw core are src*n bet tcr: w hcreas,,*it h four d ctcc lo rs t.lwsc are liarclly s<~e11.

(2) With five de1ectors, five modes c*an lie used, which gives a better cliance of having a com-p()]wnt with n peak in the right location.

This is illustrated iu Figs. 2 and :L Figure 2 shows the worst curve that occurred during a transient with four detectors, and Fig. 3, the same worst curve with five detectors.

In view of this success, a representative sample of 25 axial power shapes from three-dimensional calcula-tions were analyzed with fotlf, five, and six equally 2.0 1.6 1.2 0.8 0.4 i

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the same as before wiLli Ll1c six delccLors bcillg centered at 10, 26, 4.2, 58, (.I., and 90% or the core height.

Again, the houncfary r.onditirins wPrt> se]'.)ct<~d to µ-i,rc* H mean error in the axial peak-lo-a \\*ernge pow.~r ratio of about zero.

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0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 FRACTION OF CORE HEIGHT Fig. 4: Typical shapes from three-dimensional analyses The results of the analysis are shown.in Table II.

Again the improvement in going from four to five detectors is apparent, as well as lhe limited extra gain in going to six detectors. The largest error occurs in a box which has very low power, since-it is almost fully rodded, hut which has distorted power distributions in the bottom 103 of tlie core below lhe rod. This is illustrated in Fig. 5 for the various cases. Such a box would not be a limiting case.

These results indicate that a five detector system is better than a four detector system,* and tliat a six det.cct.or system docs not give significant further gains.

Ti1ese *results are -borne out whc11 the entire set of 811.6 one-and three-dimensional shupes w<~re consid<~rr~d.

With fiv.e deleelors, a single value of B was used lo ohlnin the rc~sults givq1 in Tnhlc~ llL For 1.hP fo11r det.ccl.or system, the best. valtH~s of' B were. use.cl for

TABLE II ERROR ANALYSISt OF THE AXIAL PEAK TO AVERAGE POWER RATIO FOR 3-D AXIAL SHAPES Case 4 detectors...................................................

5 detectors...................................................

' 6 detectors...................................................

real* fit t % error = --- X 100 real Mean Error, %

-0.2

-0.1

-0.1 Standard Deviation,%

2.9 1.4 1.2 Maximum Error, %

+12.5

-6.0

-3.7 TABLE Ill ERRORt ANALYSIS OF THE AXIAL PEAK TO AVERAGE POWER RATES FOR ALL SHAPES Case Mean Error,%

Standard Deviation,%

1.4 Maximum Error, %

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0.1 5 detectors...................................................

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 FRACTION Of CORE HEIGHT Fig. 5: Comparison of four and five detector synthesis.

• for a bottom peaked distribution each set of curves, i.e., a different value for each time in life. With five detectors, there is little variation of the boundary condition with life. The expected standard deviation in the error in fitting the axial peak to average power is about 0.83.

These results were all obtained with the smooth power distrilmlions typical of C-E reactors, which have 3

110 sizeable loeal depressious due to Inconel grids. etc:.

If such grid effccLs are present, the results would deteriorate somewhat. Standard deviaLions of the error in the peak-to-average power ratio could increase by some 0.5 to 13.

CONCLUSIONS The concept of synthesizing axial power distributions from a limited number of detector readings with Fourier expansion modes is a viable concept.*. A five detector system leads to expected standard deviations in the accuracy of the peak to average power ratio of ahoul 0.83. In addition, a unique fitting parameter in the form of an extrapolation distance can be determined which is valid for all times in life. The five detector system, thus, represents an advance over the four detector. system, while a six detector system does not bring further significant gains.

• Other methods (e.g., spline) for fitting the data were tried. None were consistently heller limn the Fourier approach.

HEFERENCES

1. H. L. HELLENS, T. G. OBER, R. D. Omm, "A Method of Analyzing In~core Deleclor Data on Power Re-actors," Trans ANS, 12, 320 (1969).

2. T. G. OBER, P. H. GAvrN, "Use of In-core Instru-mentation in Combustion Engineering Power Re-actors," Trans ANS, l9, 213 (l97cf.); for complete paper: Cornhusl.ion Engineering Publication TIS-

• l.271.

i. T. C. ()131-:a, \\V. B. T1rnNEY. r;. 1-l..\\L\\flK:-;. 'TYCA Method of Analyzing In-core Deter.tor Data in Power Reactors," CENPD-145, Combustion Engineering, Inc. (1975).

4. W. B. TERNEY; T. G. Ourm, E. A. WILLIAMSON, JR.,

"Three Dimensional Calculation.al Vcr(fication of C-E's In-core lnslrwnentalion System with Lifetime,"

Trans ANS, 21, (1975); for complete paper: Com-lmstion Engineering Publication TIS-it719.

<>. M. M. L1*;v1N1*;, D..J. D1ANIOND, "Reactor Power Dislribnlion from Analysis of In-core Defector Read-ings," Nucl. Sci. Eng., 47, 415 (1972).

6. A. JONSSON, "Fourier Expansion as an Aid in the Solution of the Diffusion Equation for Three Dimen-sional Power Distributions in Water Reactors,"

Annals of N uclcar Energy, 2, 17 (1975).

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