Improved corner neutron flux calculation for Start-up Range Neutron Monitor

Proceedngs of Internatonal Symposum on EcoTopa Scence 2007, ISETS07 (2007) Improved corner neutron flux calculaton for Start-up ange Neutron Montor Masato Watanabe 1, Hdetsugu Okada 1 and Yosho Kmura 2 1. Chubu Electrc Power Co., Inc., Nagoya, Japan 2. Chuden Computer Technology Integrator Co., LTD., Nagoya, Japan Abstract: We calculated Startup ange Neutron Montor () response durng refuelng n a bolng water reactor (BW). The fxed source problem of a dffuson equaton s solved by the 4th order nodal expanson method (NEM). A method for calculatng response was devsed. The new method for calculaton of corner flux at postons s expandng ntra nodal flux by drectly usng a 4th order nodal expanson coeffcent. Compared wth smulated reference data, the new method s more accurate because the exstng method s only multplyng the corner dscontnung factor and node average flux. Keywords: BW,, fxed source problem, NEM, neutron emsson rate 1. INTODUCTION In a BW, sub-crtcalty montorng under refuelng s carred out by the start-up range montor (). In order to dagnose that the tself s sound, the plant techncal specfcaton requests that the countng rate of s be always over 3[cps] when nuclear fuels exst n the core. The purpose of ths study s to estmate response more accurately. Accurate estmaton saves several hours of refuelng procedure because, n order to ncrease the countng rate, we often locate a number of spent fuels (SFs) that are temporarly adjacent to the as strong neutron sources. Accurate estmaton reduces the number of temporarly located SFs. In ths study, a verfcaton of an mproved corner neutron flux calculaton method s carred out by means of comparng the detaled fne-mesh fxed source calculaton. 2. METHOD 2.1 Scheme of response calculaton The calculaton of response s a fxed source problem of neutron dffuson theory for the whole core. We use the fourth order Nodal Expanson Method (1) code MOSA-Lght (2) shows our scheme of response calculaton n Table 1 and Fg. 1. Nuclear constant (3) and nuclde composton were calculated wth plant process computer. The neutron emsson rate was calculated wth SOUCES4A (4). response for all refuelng steps was calculated usng these constants. 2.2 Exstng method of calculatng response The s are set on the corner of fuel bundles, at the so-called narrow-narrow gap. Evaluatng response means calculatng the corner flux at the narrow-narrow gap. To calculate the corner flux, we usually use Eq. (1), as when calculatng Local Power ange Montor (LPM) response, regardng the evaluaton of core power dstrbuton (5). φ = φ f NM, (1) Corner 0 S where φ 0 : Average flux at -th node, whch s obtaned by Nodal Expanson Method f : The rato of flux at poston and nodal average flux on egenvalue problem (usual fuel assembly burnup calculaton), form factor of neutron flux on the crtcal condton at -th node Correspondng author: M. Watanabe, Watanabe.Masato@chuden.co.jp 1032

response s calculated by Eq. (2). where adjacent4bandle = α φ0 f /4, (2) α : Detector senstvty : response a x, n : -th Nodal coeffcent of 4 th order nodal expanson method at -th node φ ( x) φ ( y) φ ( z) φ ( xyz,, ) = (4) V V : Volume at -th node ( φ ) 2 o It s well known that evaluatng the corner flux by φ = φ( x, y, z ) Corner (5) usng Eq. (2) on a crtcal core of full power operaton acheves good accuracy. But we fnd that the accuracy of Eq. (2) s worse on the condton of sub-crtcal cores, fxed source problems, and small cores n the ntal stage of refuelng. Four fuel bundles are set around each at frst, whch s smlar to a small core. The cause of the accuracy deteroraton estmated that the flux gradent s very steep on the small core and sub-crtcal condton, so can not be regarded as a steep flux gradent nsde a calculaton unt volume (-th node). Based on the above fact, we searched for a remedy. f 2.3 New method of calculatng response In order to evaluate the corner flux more accurately, we expanded ntra nodal flux by drectly usng 4 th order nodal expanson coeffcent from Eq. (3) to Eq. (6) (6). Ths method s a substtuton of the well-known pn power reconstructon method (7). Moreover, t s easer to calculate ntra nodal flux than perform the pn power reconstructon method. where φ ( x) 4 φ0 xn, n= 1 n φ ( x) a x, = + (3) : X-drecton ntra-nodal flux dstrbuton under averaged y-z surface n -th node Corner φ : Corner flux at poston at -th node adjacent 4bandle Corner = α φ /4, (6) Note that there s no flux-dscontnung factor n Eq. (6). Normally, dscontnuty factor s calculated n a bundle calculaton on the nfnte (reflectve) condton. We beleve that ths factor s not approprate for usng n a small core. Therefore, n ths paper we do not use flux-dscontnung factor n the core calculaton. Features of the new method and ordnal one are summarzed n Table 2. 3 ESULTS OF ANALYSIS 3.1 Descrpton of reference calculaton The reference calculaton was carred out n order to confrm the effect of the mprovement. Ths calculaton uses a fne mesh fxed source and heterogamous geometry of the fuel bundle. A core map for reference calculaton around s shown n Fg. 2 and calculaton condton s shown n Table 3. Note that the new method of calculatng response s smulated by a fne mesh calculaton wth homogenous geometry. Therefore, the neutron flux dstrbuton of the new method s slghtly affected by the pn power reconstructon method. 1033

3.2 Comparson between new method and exstng method Table 4 shows a comparson between the rato of reacton rate 4/1 s of the new and exstng methods, as defned n Eq. (7). 4/1 s ntroduced for easy comparson. Neutron flux dstrbuton s shown n Fg. 4. at four bundlesloadng 4/1 = (7) at onebundleloadng Usng the ordnal method led us to overestmaton of the predcted 4/1, whch n turn led us to un-conservatve estmaton when confrmng response over 3cps pror to refuelng. Approxmately two tmes was ths overestmaton observed. The reason for overestmaton of 4/1 s perhaps as follows: Comparng Fg. 4-a and Fg. 4-b of four bundles loadng, the thermal neutron flux of homogenzed geometry n Fg. 3-b s well reflected by the water reflector. Consequently, the absolute neutron flux level of four bundles loadng at homogenzed geometry s rather hgher than that of heterogeneous geometry (reference). Comparng Fg. 3-a and Fg. 3-b of one bundle loadng, neutron flux dstrbuton of the mproved method n Fg. 3-b s not smulated exactly as per the reference neutron flux dstrbuton of Fg. 3-a. The slope from to the control rod n Fg. 3-a s not seen n Fg. 3-b. The thermal neutron flux dstrbuton of Fg. 3-b s perfectly symmetrcal, so the level of thermal neutron flux at one bundle loadng s underestmated by the ordnal method. Consequently, the two aforementoned reasons may cause the overestmaton of 4/1. The mproved method, however, shows a conservatve estmaton of response calculaton and mproves the accuracy of the corner neutron flux calculaton. Approxmately half of the tme underestmaton s observed. elatve estmaton error s reduced to about 50% by the new method. The accuracy of predcton s stll not good, however, so further study s requred. The cause of predcton error may be found n the one bundle reloadng calculaton. For one bundle loadng, a proper correcton of the cross-secton s needed for reproducng the result of a fne-mesh fxed source calculaton (reference). 4 CONCLUSION In ths study we propose a new method of calculaton of corner flux at poston: expandng ntra nodal flux by drectly usng 4th order nodal expanson coeffcent. Ths method s effectve under condtons of fxed source problems n small cores, especally durng the ntal state of refuelng, when compared wth multplyng the form factor and node average flux. However, t s rather dffcult to calculate the neutron flux of a one bundle loadng system wth a control rod nserted by the 4th order nodal method. Further study for the calculaton of one bundle loadng s requred. EFEENCES 1 Fnnenmann B., Bennewtz F. and Wagner M..,"Interface Current Technques for Multdmensonal eactor Calculatons", Atomkernenerge, 30, 123 (1977) 2 Okumura K., MOSA-Lght; Hgh Speed Three-Dmensonal Nodal Dffuson Code for Vector Computers, JAEI-Data/Code 98-025 (1998), [n Japanese]. 3 T. Iwamoto, M. Yamamoto, An Improved One-and-a-Half Group BW Core Smulator for a New-Generaton Core Management System, J. Nucl. Sc. Technol., 37, 26 (2000). 4 W.B. Wlson,. T. Perry, W. S. Charlton, T. A. 1034

Parsh, G. P. Estes, T. H. Brown, E.D. Arthur, M. Bozoan, T.. England, D. G. Madland,J. E. Stewart, "SOUCES 4A: A Code for Calculatng (α,n) Spontaneous Fsson, and Delayed Neutron Sources and Spectra," LA-13639 (1999) 5 Iwamoto, T., Yamamoto, M., Pn power reconstructon methods of the few-group BW core smulator NEEUS, J. Nucl. Sc. Technol. 36, 1141 1152(1999) 6 M. Watanabe, H. Okada and Y. Kmura, Analyss of Startup ange Neutron Montor () esponse Durng efuelng n BW, 15th Internatonal Conference on Nuclear Engneerng Nagoya, Japan, Aprl 22-26, ICONE15-10151 (2007) 7 K. Koebke and L. Hetzelt, On the econstructon of Local Homogeneous Neutron Flux and Current Dstrbutons of Lght Water eactors from Nodal Schemes, Nucl. Sc. Eng., 91,123-131(1985) 1035

Table 1 Scheme of response calculaton (Smulated) Plant Process Computer esponse calculaton Output emarks Name of calculaton code Nuclear constant Neutron emsson rate Corner neutron flux at The combnaton of whole core calculaton and bundle calculaton Fxed source problem for whole core of whch calculaton for corner neutron flux s mproved. LOGOS SOUCES4A (Modfed) MOSA-Lght Table 2 Method for calculatng corner neutron flux Improved method Ordnal method eference Descrpton Expandng ntra nodal flux by drectly usng a 4th order nodal expanson coeffcent In the present study, ths treatment s smulated by the core calculaton of fne mesh and homogeneous geometry Multplyng the corner-dscontnung factor (TIP coeffcent) and node average flux Calculatng corner neutron flux by the core calculaton of fne mesh and heterogeneous geometry Table 3 Calculaton condton of vrtual refuelng Descrpton Fuel type 8x8 BW fuel at 30GWd/st, vod hstory s 40% In the present study, the neutron emsson rate of each fuel pn n the bundle s assumed to be the same Core geometry 4x4 fuel bundles system where all control rods are nserted, cold condton of 20 C No use of flux-dscontnung factor Boundary condton xy-drecton: vacuum, z-drecton: refractve response In the present study, response s assumed to be proportonal to thermal flux only Procedure of refuelng Four lke fuels are sequentally loaded around the Table 4 esults of mproved method and ordnal method 4/1 elatve value of reference Improved method 1.891 49% Ordnal method 7.558 197% eference 3.837 100% 4/1 means the rato of the response between one fuel beng loaded and four fuels loaded 1036

Plant Process Computer response calculaton Nuclear constant Neutron emsson rate Procedure of refuelng response Improved corner neutron flux calculaton Fg. 1 Scheme of response calculaton (2-a) Detaled geometry (2-b) Homogenzed geometry Four bundles are loaded One bundle s loaded (eference) (Proposed method) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 52 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 51 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 50 38 38 38 38 38 38 38 38 38 38 38 39 39 39 39 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 39 39 39 39 38 38 38 38 38 38 38 38 38 38 38 49 38 38 38 38 38 38 38 38 38 38 38 44 48 48 44 38 38 38 38 38 38 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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Fg. 2 Example of calculaton geometry for response durng refuelng Corner neutron flux means central average four fne mesh of present system (green area) The number n the mesh means materal number. Dfferent number means usng dfferent nuclear constant. 1037

(3-a) Heterogeneous geometry Thermal energy group (3-b) Homogenzed geometry Thermal energy group (3-c) Heterogeneous geometry Frst energy group (3-c) Homogenzed geometry Frst energy group Fg. 3 Neutron flux dstrbuton (one fuel bundle s loaded) 1038

(4-a) Heterogeneous geometry Thermal energy group (4-b) Homogenzed geometry Thermal energy group (4-c) Heterogeneous geometry Frst energy group (4-c) Homogenzed geometry Frst energy group Fg. 4 Neutron flux dstrbuton (four fuel bundles are loaded) 1039