Meysam MOHAMMADNIA 1*, Ali PAZIRANDEH 1, and Mostafa SEDIGHI 2

Transcription

1 M. Moaadnia, et al.: De vel op ent of a Co puter Code for Neutronic... Nu clear Tec nol ogy & Ra di a tion Pro tec tion: Year, Vol. 8, No., pp DE VEL OP MENT OF A COM PUTER CODE FOR NEUTRONIC CAL CU LA TIONS OF A EX AG O NAL LAT TICE OF NU CLEAR RE AC TOR US ING TE FLUX EX PAN SION NODAL METOD by Meysa MOAMMADNIA *, Ali PAZIRANDE, and Mostafa SEDIGI Departent of Nuclear Engineerin Science and Researc Branc, Islaic Aad University, Teran, Iran OCE, Ofog Consulting Engineering Copany, Teran, Iran Sci en tific pa per DOI:.8/NTRP7M Te flux ex pan sion nodal etod is a suit able etod for con sid er ing nodaliation ef fects in node cor ners. In tis pa per we used tis etod to solve te intra-nodal flux an a lyt i cally. Ten, a co puter code, naed MA.CODE, was de vel oped us ing te C# pro gra ing lan - guage. Te code is ca pa ble of re ac tor core cal cu la tions for ex ag o nal ge o e tries in two en ergy groups and tree di en sions. Te MA.CODE i ports two group con stants fro te WIMS code and cal cu lates te ef fec tive ul ti pli ca tion fac tor, ter al and fast neu tron flux in tree di en sions, power den sity, re ac tiv ity, and te power pea ing fac tor of eac fuel as se bly. Soe of te code's er its are low cal cu la tion tie and a user friendly in ter face. MA.CODE re sults sowed good agree ent wit IAEA bencars, i. e. AER-FCM- and AER-FCM-. Key words: flux ex pan sion nodal etod, ex ag o nal ge o e try, neu tron flux dis tri bu tion, MA.CODE IN TRO DUC TION Te reactor core is a eterogeneous ediu wit a li ited sie. Wen neu trons are dis trib uted troug out te core, tey ay be ab sorbed by fuel, oderator, coolant, clad, and structural aterials, or ay lea out fro te bor ders. Te ex act so lu tion of core space equa tions is very i por tant in te cal cu la - tion of fuel burn-up and tran sient anal y sis. In or der to con vert te prob le into a o o ge neous e diu, te core is usu ally di vided into any ar eas. A large nu ber of ap prox i a tion et ods ave been de vel oped to en able a ore coputationally trac - table solution for te ective ultiplication constant and flux dis tri bu tion in re ac tor cores. Tese et ods can gen er ally be clas si fied as nodal, coarse-es, or syn te sis et ods []. Nodal et ods car ac ter ie te global neu tron flux dis tri bu tion in ters of a sall nu ber of pa ra e - ters in eac of te sev eral large re gions, or nods, into wic te re ac tor core is sub di vided for tis pur pose. Suc et ods gen er ally re quire de tailed et er o ge - neous intra-nodal flux dis tri bu tions to con struct o - og e nied pa ra e ters for eac of te any nods into wic a re ac tor core ay be di vided and to cal cu late cou pling pa ra e ters tat lin te av er age flux so lu tion in ad ja cent nodes. Global av er age nodal fluxes ust ten be co bined wit te intra-nodal et er o ge neous * Corresponding autor; e-ail:.oaadnia@iauet.ac.ir flux so lu tion if a et er o ge neous flux dis tri bu tion is re - quired []. Con ven tional nodal et ods are te first class of nodal od els. Te ba sis of suc et ods is te rep - re sen ta tion of te neu tron flux or neu tron fis sion rate witin eac of te any o og e nied fuel as se blies by a sin gle nodal av er age flux or fis sion rate tat is cou pled to te av er age flux or fis sion rate in ad ja cent nodes by te intra-nodal dif fu sion of te fast neu tron wic is rep re sented by cou pling co ef fi cients []. Te trans verse in te grated nodal etod (TINM is te sec ond class of nodal et ods. Tese et ods ave been for u lated on te ba sis of in te grat ing te -D dif fu sion equa tion over two trans verse di rec tions so as to ob tain a -D dif fu sion equa tion, wit trans - verse lea age ters, wic can be solved witin a node by ap prox i at ing te de pend ence on te re ain - ing spa tial vari able, usu ally wit a poly no ial. Tese et ods are con sis tently for u lated in tat tey re - duce te liit of sall node sies to te con ven tional fi nite-dif fer ence etod for te o og e nied re ac tor odel []. Aong te, ANC- [, ] and te an a lyt - i cal func tion ex pan sion nodal (AFEN etod [4, 5] are ost no tice able. Tey bot eli i nate te dif fi cul - ties of per for ing trans verse in te gra tion in ex ag o nal ge o e try and pro vide an ac cu rate so lu tion for var i ous types of re ac tors. Te ANC- code con verts ex ag o - nal ge o e try into square ge o e try and squared re la - tion sips in te Car te sian sys te. In tis etod, due

2 M. Moaadnia, et al.: De vel op ent of a Co puter Code for Neutronic... 8 Nu clear Tec nol ogy & Ra di a tion Pro tec tion: Year, Vol. 8, No., pp to te con ver sion of ex ag o nal to square, te Jacobi el - liptic function is difficult to establis [6]. Te AFEN etod di rectly solves ulti-group neu tron dif fu sion equa tions and its re sponse to te sep a ra tion of an a lytic func tions can be con sid ered, wile neu tron dif fu sion equa tions ave a good ac cu - racy of so lu tions in all parts. Te sur face av er aged flux and six points' cor ner fluxes are con sid ered te cou - pling nodal bound ary con di tions. In tis etod, due to te ad di tion of bound ary con di tions, co pu ta tional coplexity increases [6]. In flux ex pan sion nodal etod (FENM, te intra-nodal fluxes were ex panded into a set of an a lytic ba sis func tions for eac group. Tey i proved te nodal cou pling re la tions and a new type of nodal bound ary con di tions wic re quire te con ti nu ity of bot te ero- and first-or der o ents of par tial cur - rents across te nodal sur faces was pro posed [6]. In tis pa per we used te FENM wit te in tro - duc tion of te vol u et ric av er age flux (j total. Ta ing into ac count te ex ter nal bound ary con di tions and te con ti nu ity of par tial cur rents in te vi cin ity of nodal sur faces, we ave cal cu lated te flux co ef fi cients for eac node. By sub sti tut ing te flux co ef fi cients in te voluetric average flux correlation, te average neu - tron flux for eac group and node was acieved in or - der to be used for te cal cu la tion of K fro te Power-Metod. Ten, a co puter code, te so-called MA.CODE, was de vel oped us ing C# to cal cu late te ter al and fast neu tron flux in tree di en sions, power den sity, re ac tiv ity and te power pea ing fac tor of eac fuel as se bly. Co pared to IAEA bencars AER-FCM-& AER-FCM-, MA.CODE re sults sowed good agree - ent. METODS OF CALCULATION Te first step in de riv ing nodal equa tions is te ex trac tion of te neu tron bal ance equa tion us ing te Boltann trans port equa tion by in te grat ing over all ov ing neu tron di rec tions, en ergy groups and te vol - ue of te node. Te a trix for of te two-group dif - fu sion equa tion in tree-di en sional ex ag o nal ge - oetry is D c j x y S t u S f S j c u Sf S j ( c D j S t u S f S x y j c u Sf S j ( By su a ri ing te above equa tions in a trix for, we ave j j c c S t S u Sf u S f S D D c c u Sf S St S u S f D D j j ( For te two groups of neu tron en ergy, c = and c =, up-scat ter ing is as sued ero (i. e. S =. Also, by now ing tat S r S t S, S r = S t S te Eigen value equa tion could be writ ten as j lj, det( li A (4 u Sf l l D D D u Sf u Sf r r S S D D D D D (5 For si pli fi ca tion, we use te fol low ing ap prox - iation us f usf S (6 S S S r r u Sf u, S S, S (7 f r r D D D D b ac 4 u S f 4 r S r (8 b l l 4 c b 4 c, ( b b In eq. (,. l and l are called fun da en tal buc ling and first ar onic buc lin re spec tively [7]. For te two eigenvalues of l, te eigenatrix A is de - fined as u Sf S us r f l [ A( l ] D D D, S l D D u ( Sf us f l [ A( l ] D D D S l D D Te aux il iary flux could be de fined as a poly no - ial [6].

3 M. Moaadnia, et al.: De vel op ent of a Co puter Code for Neutronic... Nu clear Tec nol ogy & Ra di a tion Pro tec tion: Year, Vol. 8, No., pp y lelr lelr r A le B le l ( [ ] ( Eigt in ter face par tial cur rents and first-or der o ents of te in ter face par tial cur rents as te bound - ary con di tions tat con strain intra-nodal flux dis tri bu - tions in te ex ag o nal node are sown in fig. [6]. Were ar bi trary unit vec tors are e cos ( p e e sin ( p x y,,,, 6 e e, 7 p p e cos e sin ex, 8 p p e cos e sin e y, ( If l l K and av ing e x = sin x + + cos x and e x = cos x sin x eq. ( by us ing ar bi - trary unit vec tors of eq. ( could be ex panded into te fol low ing for y ( 6 Al sin K x cos ( p ysin ( p 6 cos cos ( B K x p p l ysin ( A sin( K Z B cos( K Z 7 7 p p A 8 sin K Z cos x sin p p B K Z x 8 cos cos sin A sin K p p Z cos ysin p p B cos K Z cos ysin ( If l l i l ik and now ing tat e ix = cos x + i sin x and e ix = cos x i sin x, eq. by us ing ar bi trary unit vec tors of eq. would be y ( 6 Al sin K x cos ( p ysin ( p 6 p B l sin K x cos ( ysin ( p A7 sin( K Z B7 cos( K Z p p A K Z x 8 sin cos sin p p B 8 cosk Z cos x sin p p A sink Z cos ysin p p B cosk Z cos ysin (4 Fro eqs. ( and ( for te two groups of neu tron en ergy in two odes, te fol low ing for ula is ob - tained u Sf us f l D D D S l D D S A SN ( K e S B CS ( K e = = S A SN ( K e S B CS ( K e = = u us f l D D D S l D D S A SN ( Ke S B CS ( Ke = = S A SN ( Ke S B CS ( Ke = = (5 Te so lu tion of eq. (5 leads to four sets of two equa tions in wic four equa tions ust be ero S S r A A D l D S S r A A D D l S S r B D B l D S B B S l r D D (6 Fig ure. Co-or di nate sys te for te ex ag o nal node Te so lu tions to eq. (6 are

4 M. Moaadnia, et al.: De vel op ent of a Co puter Code for Neutronic... 4 Nu clear Tec nol ogy & Ra di a tion Pro tec tion: Year, Vol. 8, No., pp A B D l r S A B A B R D l r A B (7 Te re la tion be tween te aux il iary flux and te intra-nodal flux is j ( X, Y, Z R S j X Y Z (,, A SN ( K e B CS ( K e A SN ( Ke B CS ( Ke (8 In tis equa tion, te intra-nodal flux is on te left and te sec ond a trix on te rigt side of te equa tion is te aux il iary flux. Eig teen un nown co ef fi cients for A l and B l, in two odes ( =, = and two en ergy groups are ob tained fro te an a lyt i cal in te gra tion of eq. (8. Te bound aries of te sur face integrals are in tro duced in fig.. Ac cord ing to te in te gral bound aries, eq. (8 for sur face nu ber and for odes and be coes r j g, d R A SN ( K e B CS ( K e S A SN ( Ke B CS ( Ke d y r j g, ( d x R A SN ( K e B CS K e r ( S A SN ( Ke B CS ( Ke dy + d( x R A SN ( K e B CS ( K e S A SN ( Ke B CS ( K e r d y x ( ( For te pur pose of con cise ness, cor re la tions for sur faces -6 are not given ere. Coicients for A and B fro te above equa - tions are de fined by us ing new pa ra e ters naed gaa fac tors. Te said gaa fac tors are in tro - duced in or der to ben e fit fro te sy e try of te ex ag o nal node. Tey are func tions of K (buc ling ode and (pitc. p p sin U, cos U 4 p p sin U, cos Y 4 4 ( For ode, te afore en tioned A and B co ef - fi cients are given in tab.. r For calculating j g wen l ( l we ave, to add te re sults of ul ti pli ca tion of te first col un by te sec ond (tird col un for eac row. Tis is te case wit oter ta bles as well. Te av er age sur face cur rent for ode and for sur face can be writ ten as J r Dg d f ( x, y, g x x dy ( Table sows current coicients for A and B. f D r g J ( d g x x fg dy d( x x dy ( Cor re la tions for te flux and cur rent for te up - per sur face (+ and te lower sur face ( wit teir in te gral bound aries sowed in figs. and are Z j g, x x R d A SN ( K e B CS K e r x ( S A SN ( Ke B CS ( Ke d y + Z x + dx R A SN ( K e B CS ( K e x S A SN (Ke B CS ( Ke d y (4 Z x, j, x x( R A SN ( K e B CS ( K e d x S A SN ( Ke B ( CS K e r d y Z x + dx( R A SN ( K e B CS ( K e x S A SN ( Ke B CS ( Ke dy Z (5

5 M. Moaadnia, et al.: De vel op ent of a Co puter Code for Neutronic... Nu clear Tec nol ogy & Ra di a tion Pro tec tion: Year, Vol. 8, No., pp Fig ure. In te gral boundaries of a exagonal node y, j, d x x( R A SN ( K e B CS K e r ( S A SN ( Ke B CS ( Ke dy + d x( R A SN ( K e r B CS ( K e r x S A SN ( Ke B CS ( K e dy Z Z + dx( R A SN ( K e B CS ( K e + x S A SN ( Ke B CS ( Ke dy x Z dx( R A SN ( K e B CS ( K e S A SN ( Ke B CS ( Ke dy Z (6 J J Z Zx, J Zy, D x f dx d y Z x x f dx d y Z x D x dx( J dy x dx( J dy x x Z x Dg x( J y d d Z dx( J dy dx( J dy x Z Z d g x x Z (7 (8 x J, dy Z (

6 M. Moaadnia, et al.: De vel op ent of a Co puter Code for Neutronic... 4 Nu clear Tec nol ogy & Ra di a tion Pro tec tion: Year, Vol. 8, No., pp Ta ble. Flux coicients of first side ( = Coicient wen l > Coicient wen l < A (Y (cos Y cos Y (Y (cos Y cos Y A (Y (cos Y cos Y (Y (cos Y cos Y A (Y sin Y/ sin Y / (Y sin Y/ sin Y / A 4 (Y (cos Y cos Y (Y (cos Y cos Y A 5 (Y (cos Y cos Y (Y (cos Y cos Y A 6 (Y sin Y/ sin Y / (Y sin Y/ sin Y / A 7, A A 8 ( sin Y sin Y / ( sin Y sin Y / 4 4 B (Y (sin Y sin Y (Y (sin Y sin Y B (Y (sin Y sin Y (Y (sin Y sin Y B (Y cos Y/ sin Y / (x cos Y/ sin Y / B 4 (Y (sin Y sin Y (Y (sin Y sin Y B 5 (Y (sin Y sin Y (Y (sin Y sin Y B 6 (Y cos Y/ sin Y / (Y cos Y/ sin Y / B 7 ( sin B 8 ( sin Y cos Y Y ( sin 4 4 B ( sin Y sin Y/ 4 Y ( sin Y cos Y / 4 4 ( sin Y sin Y/ 4 Ta ble. Cur rent co ef fi cients of first side ( = l > l < A cos p/(y (sin Y sin Y cos p/(y (sin Y sin Y A cos p/(y (sin Y sin Y cos p/(y (sin Y sin Y A cos p / 4 ( Y cos Y / sin Y/ cos p / 4 ( Y cos Y / sin Y/ A 4 sin / ( Y (sin Y sin Y sin / ( Y (sin Y sin Y A 5 sin / ( Y (sin Y sin Y sin / ( Y (sin Y sin Y cos / ( Y cos Y / sin Y/ cos / ( Y cos Y / sin Y/ A 6 A 7, A A 8 sin Y cos Y / sin Y cos Y / 4 4 B cos p/ ( Y (cos Y cos Y cos p/(y (cos Y cos Y B cos p/(y (cos Y cos Y cos p/(y (cos Y cos Y B cos / ( Y sin Y / sin Y/ cos / ( Y sin Y / sin Y/ B 4 sin / ( Y (cos Y cos Y sin / ( Y (cos Y cos Y B 5 sin / ( Y (cos Y cos Y sin / ( Y (cos Y cos Y B 6 cos / ( Y sin Y / sin Y/ cos / ( Y sin Y / sin Y/ B 7, B B 8 sin Y sin Y / sin Y sin Y / 4 4 Equa tion sows te av er age par tial cur rent in te two odes and two groups of neu tron en ergy for te six lat eral sur faces of te ex ag o nal node, wile eq. ( is for te up per and lower sur faces. r, J, r, r, Fg, J, g,,,,,, 6 4 (, J,,, Fg, J, g,,,,, 4 ( J and J as te ero and first o ent of te in - ter nal and ex ter nal cur rents are de fined in eqs. ( and ( in wic G and G are con stant a trixes wose ar rays de pend on K and node group dif fu sion. C is a a trix wic de fines intra-nodal flux co ef fi cients J J G C ( G C ( Ma trix C is cal cu lated in an it er a tive pro cess be - tween eqs. ( and (. J in eq. ( de pends on ex - ter nal bound ary con di tions and ex ter nal cur rents fro neig bor ing nodes. We used te Gauss eli i na tion

7 M. Moaadnia, et al.: De vel op ent of a Co puter Code for Neutronic... Nu clear Tec nol ogy & Ra di a tion Pro tec tion: Year, Vol. 8, No., pp etod to de ter ine C in eq. (. Ten, by sub sti tut - ing a trix C in eq. (, ex ter nal par tial cur rents were cal cu lated. Te ex ter nal cur rents fro te node are te in ter nal cur rents of te neig bor ing nodes. Fi nally, te vol u et ric av er age flux for te ex - ag o nal node is ob tained in eq. (4 by sub sti tut ing te flux co ef fi cients in te vol u et ric av er age flux cor re - la tion; te av er age neu tron flux for eac group and node is acieved in or der to be used for te cal cu la - tion of K fro te power-etod. x x j total ( 4 R ASN ( Ke BCS ( Ke S A SN ( Ke B ( CS Ke r dxdyd x + R ASN ( Ke B CS ( Ke x S A SN ( Ke B CS ( Ke dxdyd (4 Fig ure 4. Main win dow of te MA.CODE Fig ure 5. Core con fig u ra tion in te MA.CODE Te wole pro ce dure for te MA.CODE is setced in te flowcart of fig.. In a user friendly en vi ron ent, te MA.CODE re quires a nu ber of nodes in te ra dial and ax ial di - rec tions, as well as te lat tice pitc and bound ary con - di tions for ex ag o nal nodes. Te code is cou pled wit WIMS D5 and reads te cross-sec tions fro WIMS autoatically (see fig. 4. Te core con fig u ra tion setced in te MA.CODE can be seen in fig. 5. CONCLUSION AND DISCUSSION Fig ure. Flowcart of MA.CODE In tis pa per we ave used te FENM wit te in tro duc tion of te vol u et ric av er age flux (j total.

8 M. Moaadnia, et al.: De vel op ent of a Co puter Code for Neutronic Nu clear Tec nol ogy & Ra di a tion Pro tec tion: Year, Vol. 8, No., pp Fig ure 6. Co par i son be tween MA.CODE re sults wit AER-FCM- (Scul bencar Ta ing in con sid er ation te ex ter nal bound ary con di - tions and te con ti nu ity of par tial cur rents in te vi cin - ity of nodal sur faces, we ave cal cu lated te flux co ef - fi cients for eac node. By sub sti tut ing te flux coicients in te voluetric average flux correlation, te av er age neu tron flux for eac group and node is acieved. Tus, K can be eas ily cal cu lated fro te Power-Metod. By te an a lyt i cal so lu tion of te integrals of flux and cur rent on te sur face of te ex ag o nal node wit re spect to fig., fig., and eqs. ( to (, us ing te sy e try of te ex ag o nal node and con sid er ing eq. (, we ave ob tained sig nif i cant re sults con cern ing te re la tion be tween te flux and cur rent co ef fi cients us ing te buc ling ode. In two par al lel node sur faces, A flux and cur rent co ef fi - cients in, (l and l are sy et ric and B flux and cur rent co ef fi cients are equal, but in tis is re verse. For te sae of bencarin we ave co - pared te re sults fro te flux ex pan sion nodal etod (FENM us ing our code (MA.CODE wit two IAEA bencars, i. e. AER-FCM- [8], also nown as te Scul benc ar and AER-FCM- [], nown as Seidel's benc ar. Te FENM etod pro posed in tis pa per sows a good agree ent wit tese two bencars. Te ective ultiplication factor for te Scul benc ar was.45, wile our code cal cu lates.4848 (i. e..% er ro. Te co par i son be tween MA.CODE fuel assebly relative power densities wit te AER-FCM- benc ar is given in fig. 6. Rel a tive power den si ties fro te MA.CODE and AER-FCM-bencar for fuel as se bly no. are also co pared in fig. 7. Fig ure 7. Co par i son be tween rel a tive power den si ties fro MA.CODE wit AER-FCM- (Scul benc ar for fuel as se bly no. Te ective ultiplication factor for Seidel's benc ar was.47, wile our code cal cu lates.4 (i. e..6% er ro. Te co par i son be tween te MA.CODE fuel as se bly rel a tive power den si ties and te AER-FCM- benc ar is given in fig. 8. Rel a tive power den si ties fro te MA.CODE and AER-FCM-bencar for fuel as se bly no. are also co pared in fig.. AUTOR CONTRIBUTIONS Te te o ret i cal anal y sis was car ried out by M. Moaadnia and A. Pairande. An a lyt i cal so lu - tions of te equa tions and C# pro gra ing co puter code were car ried out by M. Moaadnia. Te anu script was prepared by all au tors and te fig ures and ta bles by M. Moaadnia and A. Pairande.

9 M. Moaadnia, et al.: De vel op ent of a Co puter Code for Neutronic... Nu clear Tec nol ogy & Ra di a tion Pro tec tion: Year, Vol. 8, No., pp Fig ure 8. Co par i son be tween MA.CODE re sults wit AER-FCM- (Siedel's benc ar (OS CAR Fig ure. Co par i son be tween rel a tive power den si ties fro MA.CODE wit AER-FCM- (OS CAR benc ar for fuel as se bly no. REF ER ENCES [] Stacey, W. M., Nu clear Re ac tor Pys ics, Jon Wiley & Sons Inc., New Yor, USA, 7 [] Co, N. Z., No, J. M., An a lytic Func tion Ex pan sion Nodal Metod for ex ag o nal Ge o e try, Nucl. Sci. Eng.. (5, pp [] Cao, Y. A., Satilla, Y. A., Conforal Map ping and ex ag o nal Nodal Met ods II: I ple en tation in te ANC- Code, Nucl. Sci. Eng., (5, pp. -5 [4] No, J. M., Co, N. Z.,???, Proceedings, International Con fer ence on te Pysic of Re ac tors (PYSOR 6, Atoic En ergy So ci ety of Ja pan, (6, pp. A5- A5 [5] Cao, Y. A., Tsolfanidis, N., Conforal Map ping and exagonal Nodal Metods I: Mateatical Foundation, Nucl. Sci. Eng., (5, pp. - [6] Xia, B., Xie, Z., Flux Ex pan sion Nodal Metod for Solving Multi-Group Neutron Diffusion Equations in exagonal- Geoetry, Ann. Nucl. En ergy, (6, pp [7] Downar, T., Lee, D., Xu, Y., Kolowsi, T., Te ory Man ual for te PARCS Neutronic Core Si u la tor, PARCS, U.S. NRC,.6, 4 [8] Scul, G., So lu tions of a -D VVER- Benc - ar, Proceedings, 6 t Sy po siu of AER on VVER Re ac tor Pys ics and Safety, Kironui, Fin land, 6 [] Seidel, F., Dif fu sion Cal cu la tions for VVER-44 D and D Test Prob le, Proceedings, 4 t Syp. of TIC,, 85, p. 6 [] Pairande, A., et al., Developing a Nuclear Neutronic Code in Rectangular, Triangular and Cylindrical Geoetry, Jour nal of Nu clear Sci ence and Tec nol ogy, 6 (, pp ( [] Moaadnia, M., et al., Design a Coputational Progra to Calculate te Coposition Variations of Nuclear Materials in te Reactor Operations, Annals of Nuclear Energy, 57 (, pp. - Re ceived on Jan u ary, Ac cepted on Au gust,

10 M. Moaadnia, et al.: De vel op ent of a Co puter Code for Neutronic Nu clear Tec nol ogy & Ra di a tion Pro tec tion: Year, Vol. 8, No., pp Mejsa MOAMADNIJA, Ali PAZIRANDE, Mostafa SEDIGI RAZVOJ PROGRAMA ZA NEUTRONSKE PRORA^UNE JEZGRA NUKLEARNOG REAKTORA SA EKSAGONALNOM ]ELIJOM METODOM NODALNOG RAZVOJA FLUKSA Metoda nodalnog ravoja flusa pogodna je a raatrawe efeta nodaliacije u nodni uglovia, a u ovo radu ori{}ena je a analiti~o re{avawe e unodalnog flusa. Na ovoj osnovi ravijen je ra~unsi pro gra pod ieno MA.CODE u prograso jeiu C#. Pro gra je osposobqen a prora~un reatorsog jegra sa esagonalno geoetrijo }elije, u dve energetse grupe i tri dienije. Prograo MA.CODE preuiaju se dvogrupne onstante i prograsog paeta WIMS i ira~unavaju efetivni fator uno`avawa, flusevi teralni i bri neutrona u tri dienije, gustina snage, reativnost i fator pia snage a svai gorivni ansabl. Me u vrlinaa prograa su brina prora~una i jednostavan orisni~i pristup. Reultati prograa MA.CODE dobro se sla`u sa IAEA testovia, na prier, AER-FCM- i AER-FCM-. Kqu~ne re~i: nodalna etoda, esagonalna geoetrija, raspodela neutronsog flusa,...ma.code