D5 REAL-TIME MONITORING OF POWER AND NEUTRON CAPTURE CROSS SECTION IN NUCLEAR RESEARCH REACTOR D.A.P. PALMA Brazilia Nuclear Eergy Commissio (CNEN), Rio de Jaeiro, Brazil A.Z. MESQUITA, R.M.G.P. SOUZA Nuclear Techology Developmet Cetre (CDTN), Belo Horizote, Brazil A.S. MARTINEZ Nuclear Eergy Program, PEN COPPE/UFRJ, Rio de Jaeiro, Brazil Abstract Nuclear reactor operators have to moitor the behaviour of differet uclear ad desig parameters that vary i time so to esure the safety operatio of the reactor. I recet years several operatig parameters for the IPR-R1 TRIGA research reactor were moitored ad idicated i real-time by the data acquisitio system developed for the reactor, with all the data beig stored i a hard drive i the data acquisitio computer, to build i this way a database. The goal of this work is to isert i the set of parameters already collected the eutro capture cross sectios for the fuel, from the uclear power obtaied i real-time. The experimetal data was obtaied by usig a fuel elemet istrumeted with temperature sesors, located i the core of the IPR-R1 TRIGA research reactor at the Nuclear Techology Developmet Cetre (CDTN). This iformatio is useful for the cotiuous moitorig of the eutro capture reactio rate. For that, a ew aalytical formulatio is used for the Doppler broadeig fuctio proposed by Palma ad Martiez, which is free from special fuctios i its fuctioal form ad with easy computig implemetatio. The results obtaied were satisfactory from the stadpoit of accuracy i compariso with the umerical referece model ad idicate that it is possible to carry out real-time moitorig of the eutro capture cross sectio i the fuel. 1. INTRODUCTION The movemet of thermal agitatio of the uclei is adequately represeted i the microscopic cross sectios of eutro-ucleus iteractio through the Doppler broadeig fuctio ad of iterferece term. This fuctio is calculated umerically i moder systems for the calculatio of the macrogroup costats, eeded to determie the power distributio of a uclear reactor ad is writte by: beig: dy 1 y 4 (1) x, exp x y E E x () Iteratioal Atomic Eergy Agecy 1
4 E kt / A 1/ D.A.P. Palma et al., (3) where E is the eergy of the icidet eutro, E the eergy of the resoace peak, the total width of the resoace, T the temperature of the medium ad k the Boltzma costat. Cosiderig a medium thermal equilibrium at temperature T where the target uclei are i movemet ad their velocities give by the Maxwell-Boltzma distributio ad the expressios for effective absorptio cross sectios are obtaied from the Briet-Wiger formalism [1], E E, T x,. E (4) Due the itegral form i the equatio (1), the equatio (4) is ot adequate to a real time moitorig of the absorptio cross sectio.. THE IPR-R1 TRIGA REACTOR The IPR-R1 TRIGA (Traiig, Research, Isotopes, ad Geeral Atomic), showed i Fig. 1 is a pool type uclear research reactor, with a ope water surface ad the core has a cylidrical cofiguratio []. The maximum core power is 5 kw, cooled by light water ad with graphite reflectors. The fuel is a alloy of zircoium hydride ad uraium eriched at % i 35 U. The reactor core has 63 cylidrical fuel elemets, 58 alumium- clad fuel elemets, ad 5 stailess steel-clad fuel elemets with 8.5 wt % uraium. FIG. 1. IPR-R1 TRIGA reactor pool ad core. I the ext sectio it will be preseted a ew aalytical approximatio for the Doppler x, that will allow your calculatio fast eough to make a real time broadeig fuctio moitorig of the ET, from the data of temperature ad power comig from istrumeted fuel. 3. AN ANALYTICAL APPROXIMATION FOR THE DOPPLER BROADENING x, FUNCTION The Doppler broadeig fuctio x, equatio [3], ca be defied as the solutio of differetial
,, D.A.P. Palma et al. 4 d x d x x x x,, dx dx 4 4 (5) subjected to the iitial coditios, x, x exp 1 erf 4 x, x. x (6) A aalytical expressio for the Doppler broadeig fuctio ca be obtaied by solvig the equatio (5), usig a cojuctio betwee the Frobeius method to obtai the homogeeous solutio ad the method of parameter variatio to obtai a particular solutio. The Frobeius method cosists basically of seekig solutios i the form of: h s x, c x, with c, (7) where s is a o-determied parameter which provides the method with flexibility. The replacemet of equatio (7) ad its derived elemets i equatio (11), oe obtais the followig solutio for the homogeeous equatio: h x x x x, exp k1cos ksi, 4 (8) where k ad k are costats to be determied after the impositio of the iitial coditios expressed by equatio (6). Havig obtaied the liearly idepedet solutios of the homogeeous equatio associated to Eq. (11), x x 1 x, exp cos 4 x x x, exp si, 4 (9) (1) oe ca apply the method of parameter variatio i obtaiig a particular solutio for Eq. (5), seekig solutios as: where,,, (11) p x u1 x 1 x u x x u1 x ad u x are obtaied from the coditios expressed by equatio (6). I doig so oe has the followig aalytical expressio for the Doppler broadeig fuctio: x x x, cos exp x 11 Re x, ta Im x,, 4 (1) 3
ix where x, erf. The equatio (1) provides a simple ad precise expressio for the Doppler broadeig fuctio but is possible to separate the error fuctio with complex argumet that exists i the i its real ad imagiary parts accordig to the fuctioal form of fuctio Frob x, expasio proposed by Salzer [3]. Accordig to this approximatio, the error fuctio with complex argumet ca be expaded i ifiite series: where, Re. Im., erf a bi F F i (13) a 1 cos( ab) max exp exp / 4 FRe. erf a f a, b, a 1 4a a si( ab) max exp exp / 4 FIm. g a, b, a 1 4a ad the auxiliary fuctios (14) (15) f a, b a acosh b cos ab sih b si ab, (16) g a, b acosh b si ab sih b cos ab. (17) Deotig a ad b ax ad imagiary parts: it is possible to separate fuctio x, ito its real max 1 x exp / 4 Re x, erf exp cos 1 f x,, Ap. 4 1 (18) max 1 x exp / 4 Im x, exp si g x,, Ap. 4 1 where the auxiliary fuctios f x, ad g, (19) x are re-writte by: x x x x f x, cosh cos sih si, x x x x g x, cosh si sih cos. () (1) 4
Whe replacig equatios (18) ad (19) i the expressio of the Doppler broadeig fuctio (x,ξ), equatio (1), it is possible to write the followig expressio for the Doppler broadeig fuctio: 1 x x x, exp x 1 cos 1 Re x, ta Im x, Ap.. () Ap. 4 x,, give by equatio (), is a valid expressio for all the values of Expressio for parameters x ad. I the preset paper N max =1 was used. 4. RESULTS 4.1 Thermal power moitorig Experimetal studies have bee performed i the IPR-R1 reactor by to fid out the o-lie moitorig of the core thermal power [4] ad [5]. Oe method uses the temperature differece betwee a istrumeted fuel elemet with thermocouples, ad the pool water below the reactor core. Aother method cosists of the steady-state eergy balace of the primary ad secodary reactor coolig loops. A further method is by calorimetric procedure whereby the reactor power is moitored as a fuctio of the temperature-rise rate ad the system heat capacity costat. Figure shows oe of the video-scree displays of the digital moitorig system computer that cosolidates iformatio for the reactor power status i real time. This scree moitors the power measured by the eutroic chaels ad by the ew thermal chaels. 4.. Capture cross sectio FIG. Power moitorig o the scree of the data acquisitio system. The relatio betwee the temperature i the uclear fuel as a fuctio of the power durig the operatio of the IPR-R1 TRIGA reactor ca be visualized i Fig. 3. 5
FIG. 3. Temperature i the uclear fuel as a fuctio of the power durig the operatio of the IPR-R1 TRIGA This iformatio of the temperature is useful for the cotiuous moitorig of the reactio rate i eutro capture. For that, a ew aalytical formulatio is used for the Doppler broadeig fuctio proposed by Palma ad Martiez to calculate the absorptio cross sectio that ca be visualized i the figure 4. FIG. 4. Capture cross sectio calculated from the equatio (4), i fuctio of the power measured ad the eergy of the icidet eutro. 5. CONCLUSIONS Two importat criteria for operatioal parameters measuremet i uclear reactors are redudacy ad diversity. Other criteria such as accuracy, reliability ad speed i respose are also of major cocer. The greater the umber of chaels for measurig power, the greater is the reliability ad safety of reactor operatios. The aim of this research is to develop ew methodologies for o-lie moitorig of uclear reactor power ad isert i the set of parameters already collected the eutro 6
capture cross sectios for the fuel, from the power obtaied olie. The system was implemeted, with success, i the IPR-R1 TRIGA research reactor at the Nuclear Techology Developmet Cetre (CDTN). ACKNOWLEDGEMENTS These experimets are part of a research project supported by the Brazilia Coucil for Scietific ad Techological Developmet (CNPq) ad the Research Support Foudatio of the State of Mias Gerais (FAPEMIG). REFERENCES [1] DUDERSTADT, J.J., HAMILTON, L. J. Nuclear Reactor Aalysis, Ed. Joh Wiley ad Sos, Ic. Nova York, 65 p. (1976). [] MESQUITA, A.Z. Experimetal Heat Trasfer Aalysis of the IPR-R1 TRIGA Reactor. Iteratioal Atomic Eergy Agecy (IAEA-CN-156). IAEA Publicatio - Research Reactors: Safe Maagemet ad Effective Utilizatio, v. IAEA, pp. 1-1, 8. x, [3] PALMA, D. A. P., Martiez, A.S. A Faster Procedure for the Calculatio of the Aals of Nuclear Eergy, Vol. 36, pp. 1469-1471, (9). [4] MESQUITA, A.Z.; REZENDE, H.C. Thermal Methods for O-Lie Power Moitorig of the IPR-R1 TRIGA Reactor. Progress i Nuclear Eergy, v. 5, p. 68-7. 1. doi:1.116/j.pucee.9.5.6, (9). [5] MESQUITA, A.Z.; REZENDE, H.C.; SOUZA, R.M.G.P. Thermal Power Calibratios of the IPR-R1 TRIGA Reactor by the Calorimetric ad the Heat Balace Methods. Progress i Nuclear Eergy (i press), doi:1.116/j.pucee, (11). 7