İ.T.Ü. Triga mark-II reaktöründe yakıt elemanlarının reaktivite eşdeğerlerinin iki gruplu pertürbasyon teorisi ile hesabı

Abstract

ÖZET Bu çalışmada; İ.T.Ü. TRIGA Mark-II reaktöründe bulunan yakıt elemanlarının reaktivite eşdeğerleri iki gruplu pertürbasyon teorisinden hareketle elde edilen ifadelerden hesaplanmıştır. Yakıt elemanlarının reaktivite eşdeğerlerinin hesabında gereken iki gruplu pertürbasyona uğramış tesir kesitlerinin hesabı için çalışmanın ilk bölümünde, reaktöre ait iki gruplu tesir kesitleri yakıt eşdeğer birim hücresi için yanma oranına bağlı olarak ve yakıt olmayan malzemelere ait iki gruplu tesir kesitleri ise altıgen kafeste WIMS-D/4 kodunun YVTMS-TRIGA kütüphanesi ile birlikte kullanılması ile hesaplanmıştır. Hesaplanan yakıt ve yakıt olmayan malzemelere ait iki gruplu tesir kesitlerinin deneysel sonuçlarla uyum içerisinde olduğu görülmüştür. Çalışmanın ikinci bölümünde, TRIGAP kodu önce reaktörde bulunan bölgeleri homojenleştirecek şekilde değiştirildikten sonra, yakıt elemanlarının reaktivite eşdeğerlerinin iki gruplu pertürbasyon teorisi ile hesabında gereken, reaktöre ait iki gruplu akı, ek akı dağılımları kod tarafından hesaplanarak, sözkonusu bu değerler birer polinom ile temsil edilmişlerdir. TRIGAP kodu ile yapılan hesaplarda sözkonusu kodun kullandığı giriş veri dosyalan İ.T.Ü. TRIGA Mark-II reaktöründe bulunan standart tipte ancak değişik miktarlarda uranyum içeren 1 1 tip yakıt elemanı için yanma oranına göre düzenlenmiştir. TRIGAP kodu ile hesaplanan İM gruplu akı ve ek akılar birer polinom ile temsil edildikten sonra bu polinomlar ve WIMS-D/4 kodundan yakıt ve su için elde edilen iki gruplu tesir kesitleri kullanılarak hesaplanan pertürbe edilmiş iki gruplu tesir kesitleri, iki gruplu pertürbasyon teorisinden hareketle elde edilen denklemde kullanılarak, İ.T.Ü. TRIGA Mark-II reaktöründe bulunan yakıt elemanlarının reaktivite eşdeğerleri hesaplanmış ve hesaplanan değerler, difüzyon teorisi esaslarına göre yazılan TRIGAP kodu tarafından hesaplanan değerlerle ve deneysel sonuçlarla karşılaştınlmıştir. Ayrıca bu çalışmada, yakıt elemanlarının reaktörün çalışma süresine bağlı olarak reaktivite kayıpları da hesaplanmıştır. Ancak hesaplanan değerlerin deneysel hata limitleri içerisinde kaldığı görülmüştür. XI

SUMMARY REACTIVITY CALCULATIONS FOR THE FUEL ELEMENTS OF I.T.U. TRIGA MARK-H REACTOR BY USING TWO-GROUP PERTURBATION THEORY The reactivities of the fuel elements of I.T.U. TRIGA Mark - II reactor has been calculated by using both two-group perturbation theory and a one-dimensional, two-group diffusion computer code TRIGAP. For each fuel element, reactivities calculated by both methods are compared with those measured experimentally. Both methods require the use of two-group cross-sections for the I.T.U. TRIGA Mark-n reactor core. Therefore the analysis follewed the establishes reactor physics calculational methods. The first step is to obtain two-group cross-sections for homogenized fuel and moderator mixtures and nonfuel elements such as void, a graphite element, irradiation water channel (water+graphite), a central thimble (water+void) and a graphite reflector for the I.T.U. TRIGA Mark-n reactor core. This process of the analysis is performed with the standard PC - version WIMS-D/4 code distributed by the Nuclear Agency Data Bank. There are four modules in this version of the code. The hydrogen scattering cross-section bound in zirconium-hydride is not provided in the standard WIMS cross section library. We have used the extended US version of a WIMS-D/4 library where isotopes specific to TRIGA fuel were added (Er-166, Er-167, Samarium and Hydrogen in ZrH). Among them, the scattering cross section of hydrogen in ZrH is especially important for the fuel temperature coefficient. The extended US version of a WMS-D/4 library, the following materials which were considered redundant were deleted from the library: hydrogen bound in water, deuterium bound in water, B-10, natural boron, Th-232, U-233 and some other materials. The Pi scattering matrix of deuterium has been replaced by the one for hydrogen bound in ZrHx. The transport cross sections for both new hydrogen data sets in tile fast groups were taken from the original WIMS library material 2001. The thermal data are tabulated at 293, 400, 600 and 1000 K. The data for other XHnuclides are not temperature dependent and do not include upscattering in the thermal range. The new data for hydrogen are taken from the ENDF/B-V Standarts and ENDF/B-Ht Scattering law Libraries. The data for Samarium are taken from the ENDF/B-V Fission Product Library. The data for the Erbium isotopes are taken from the ENDF/B-IV Fission Products Library. All data were processed with FEDGROUP-C several years ago. Some modifications in the code are introduced since then. Along with this library, WIMS-D/4 is used to generate an effective two-group cross-sections for the I.T.U. TRIGA Mark-II reactor. The code is used for TRIGA calculations without modifications in an 18-group unit cell approximation with adjusted critical buckling. For fuel rod containing fuel plus surrounding water, the unit cell option in WIMS-D/4 code is used, while the nonfiiel elements are treated in a cluster option, consisting of seven unit cells: a central non fissile element plus water, six fuel unit cells. The function of these fuel elements is only to provide the fission neutron source. WMS is run in the PERSEUS mode of each one of the cells that constitute the core. The volume of me unit cell and cluster is calculated so as to preserve the actual ratio between fuel and water in the core. For fuel unit cell, two-group cross-section are generated as a function of burnup. Two-group cross sections of fuel unit cells are calculated at average fuel temperature of 20 °C that is the average fuel temperature of fuel elements reactivity experiments was performed. Cross sections are also generated at average fuel temperature of 180 °C to compare these results with the results of cross- sections were obtained by using WIMS-D/4 for `Jozef Stefan` and `Dhaka` TRIGA Mark-H reactor. Agreements between calculated results for I.T.U. TRIGA Mark-H reactor and results from `Jozef Stefan` and `Dhaka` TRIGA Mark-H reactors are fairly good. Thermal group absorption and fission cross-sections of I.T.U. TRIGA Mark-n reactor were determined experimentally from the analysis of xenon poisoning experiments were performed at average fuel temperature of 100 °C. Only comparison is made for the thermal group absorption and fission cross sections with experimental data. Percentage errors for calculated thermal group absorption and fission cross sections from WIMS-D/4 code at average fuel temperature of 100 °C and are %9.98 and %SS9 respectively according to the experimental results. Unfortunately, direct comparison is not possible for the fast group cross sections because of there is no experimental results for this case. Two group flux and two group adjoint flux distributions are calculated by using TRIGAP compute code. TRIGAP and its library are modified for this purpose. XIIITRIGAP is a reactor physics code for calculations of multiplication factor, flux and power distributions in one dimensional cartesian, cylindrical and spherical geometry. It iş intended for reactor physics calculations of stationary thermal multiplying systems in two-group diffusion approximations. Besides the direct solution, the code gives also the adjoint solution of the diffusion equation. The two-group one dimensional time independent diffusion equation is solved using finite differences method. The resulting two group diffusion system is solved by die method of fission density iteration. Each group iteration is solved by Crout-Cholesky's method. After the diffusion equation is transformed to adjoint diffusion equation, and men adjoint diffusion equation can be solved in the same way of the direct diffusion equation solution. TRIGAP code consists of three data files that are namely TRIGAP.LIB, ELEM.DAT and TRIGAP.INP. TRIGAP.LIB data file contains the effective two-group cross section for all types of unit-cells (fuel and nonfuel ) for I.T.U. TRIGA MARK-II reactor core. The cross-sections of fuel unit cells are calculated at temperature of 20 °C and tabulated in dependence of burnup (in %ofU-235) from zero burnup to %9 for all type of fuel elements. The data in this file are written in the following order: Burnup and identification number of at which cross-sections of all type of fuel elements and two-group cross-section for all type of fuel elements at 15 different burnup step. ELEM.DAT file is prepared for I.T.U. TRIGA Mark-II reactor in dependence of the following data for each element: Identification number of the element, type of the element and energy produced by this element in %U-235. Identification numbers of elements can be arbitrary. Nevertheless we recommended to use the same numbers under which they are documented. For nonfuel elements we use the same numbers as for characterizing the types of those elements, because it is not necessary to distinguish between different nonfuel elements of the same type. All independent input data are entered into TRIGAP code through TRIGAP.INP file. The first parts of input data are general, specifying the geometry and other general conditions for solving the diffusion equation. In the second part the identification numbers for each fuel element in the I.T.U. TRIGA Mark-II reactor core is written. Two-group flux and adjoint flux distributions are calculated for the I.T.U. TRIGA Mark-II reactor by using modified TRIGAP code. Two-group flux and adjoint flux distributions are shown Fig.(4A), Fig.(4.5.). Shapes of the fluxes shown in Fig. (4.4.), fast neutron flux is greater than the thermal neutron flux in the core region. This is due to the fact that the core material of this reactor is more effective in absorbing thermal neutrons than in moderating neutrons out of the fast group. The peaking of 1he thermal flux arises form the slowing down in the reflector of fast neutrons that escape from the core. Since the absorption cross section of the reflector is small the thermalized neutrons accumulate in this region until they eventually diffuse back into the core, escape from the outer XIVsurface of the reflector, or are captured. Incidentally the flux peak in the reflector is much more pronounced in many reactors than that indicated in Fig. (4.4.). Spahe of the adjoint fluxes shown in Fig.(4.5.). As seen in this figure, the adjoint functions have some-what a reverse behavior from the fluxes shown in Fig.(4.4.). In particular the fast adjoint is less than the slow adjoint in the core although the fast flux is greater than the slow flux in the same region. From the discussion in Fig.(4.4.). It will be recalled that the reason why thermal flux is less than the fast flux in the core region is that the thermal absorption cross section in the core region is greater than the slowing-down cross section. As a result, the thermal flux is depressed below the value of the last flux. Viewed in a different way, the fact mat thermal absorption cross-section is greater than the removal cross-section also means that neutrons introduced into the slow group are absorbed at a greater rate and therefore contribute more directly to the chain reaction than neutron introduced into the fast group. This is equivalent to saying, neutrons added to the slow flux are more important than neutrons added to the fast group, and this is the reason why the rast and slow adjoints or importance functions have a behavior that is the reverse of that shown by the fluxes. In short, it takes more fast neutrons than slow neutrons ( more precisely, ^i,c > <&2,c) to keep the reactor critical. Neutron for neutron the slow neutrons have a greater effect on the reactor than the fast neutrons, and hence ((<l>+)i.c < (<b+h,e) as shown in Fig.(4.5.). Because of there is no experimental results for the two group adjoint and fast group flux distributions for the I.T.U. TRIGA Mark-n reactor therefore calculated two group adjoint and fast group flux distributions by using TRIGAP can not be compared with the experimental results. Only comparison is made for the average thermal group flux with experimental data. Percentage error calculated thermal group flux from TRIGAP code at power of 100 kW is % 0.5 according to the experimental results. Two-group perturbated cross sections are calculated by using the WIMS-D/4 and the results are given in Table : 5.1., Table : 5.2., Table : 5.3., Table ; 5.4. As seen in these tables perturbated thermal group absorption and fission cross sections are more effective on two-group perturbation equation according to the other perturbated cross sections. Reactivities of the fuel elements calculated by using two- group perturbation theory, TRIGAP code and experimental results are given in Table : 5.5. We have also calculated reactivities of each fuel element as a function of burnup to be found out that reactivity loss of each fuel element. Reactivity loss of each fuel element is given in Table : 5.7. As seen in Table : 5.7., average reactivity loss of each fuel element for rings B, C, D, E and F are 2.7 <t, 0.95 <j, 0.92 <t, 0.70 <2, 0.47 <£, respectively. On the other hand; total error of the fuel element reactivity worth is estimated to ± 3 <r, for all measurements. It consists of two uncorrected contributions: the error due to regulating rod position and calibration. XVBecause of this reason calculated reactivity loss of the fuel elements can not be checked experimentally. Hie results of reactivity calculations by both methods are not good agreements with experimental results. The reason for this heterogeneity of the I.T.U. TRIGA Mark-n reactor. If we wish better accuracy; we must model the I.T.U. TRIGA Mark -O reactor in three dimension explicitly. After that reactivity calculations must be performed by using both methods discussed above. XVI