Su reaktörleri için bir heterojen geometri termalizasyon hesabı yöntemi

Abstract

.dysporsium, luthencium, uranium 235 and uranium 238. The scattering and cross sections are given at 40 speed - points for H, D, U235 and U238. The absorption and fission cross sections of U235 is given at 120 speed- points. The results are compared with the results of another thermalization program previously developed, THERM. This program solves the infinite homogenious medium neutron continuity equation using Nelkin's kernel for hydrogen and deuterium and free gas kernel for oxygen. The heterogenous effects are taken into account by the Annouyal - Benoit- Horrowitz (ABH) technique. The programs are written in the FORTRAN language and and compiled and executed under both MS - DOS and LlNUX operating systems on personel computers with the PENTIUM processor. The program devoleped is called THERMP1U and written in FORTRAN language. The program is run for various water reactor unit cell problems. The thermal group homogenized parameters are calculated, along with the disadvantage factor. The results are compared with results of other programs, namely THERM, which utilizes a homogenous infinite medium calculation and ABH disadvantage factors. The effect of the moderator to fuel ratio on the disadvantage factor is also assessed. The effect of fuel oxygen and uranium thermalization on the thermal group constants are also assessed. The program is restricted to two - region cells.Hence,at its present state, the cladding region can not be treated rigorously. Hence, the program should be extended to include more than two regions. In that case, the cell could be divided into more regions and the flat flux assumption inherent in the calculation of collision probabilities could be relaxed. Also the inclusion of the zirconium hydride kernel is recommended for further work. If this is accomplished, Triga reactor thermalization calculations could be carried out. If the program could be merged with the fast spectrum program, SPEC, developed a, previously at the Institude, the slowing down sources from the epithermal region could be more VI

SUMMARY The determination of the thermal neutron spectrum is öne of the most challenging parts of the neutron spectrum calculations. This problem has a two-fold diffuculty. First, the differential scattering cross sections, called scattering kemels, must be determined. Second, the transport equation has to be solved in hetoregeneous geometry to take the heterogeneity effects into consideration. The determination of the scattering kemel is an interdisciplinary endeavour, requiring a knowledge of solid (liquid) state physics, quantum mechanics and neutron physics. By using certain simplified kernels, models have been developed for the morecommon moderators. Nelkin 's kernel, which is extensively used for the thermalization in vvater reactors, is based on a quantum mechanical model of the vvater molecule. There are also same other simplified kemels in use. The free gas kernel, which models the moderation in a monatomic gas, is öne of these simplified models. The second part of the diffıculty in the thermalization calculation is the solution of the transport equation for the unitceli. The more common approach in this stage bypassesthe heterogenous transport solution by a well- known recipe. First, the neutron continuity equation is solved for an infinite homogenous medium, characterizing the unit celi. Second the heteregeneous effects are included as corrections by the ABH method (ör less commonly by the diffusion theory method). ABH's basic function is the evaluation of the thermal disadvantege factor. The thermal spectrum is obtained by the numerical solution of the infinite medium continuity equation and then thermal disadvantage factor is btained by the subsidiary ABH method and the determination of thermal group constants is rendered possible. IIIThe solution of the infinite medium continuty equation isn't also a straightforward problem. Early treatments like the Wigner - VVilkins method, chose to transform the integral equation into a differential equations which can be more easily solved numerically. But this type of approach restricts the generality of the scattering kernels that can be used. For the transformation of the integral eguation, the scattering kemels must be kept simple in form. With the advances in computer hardvvare and software, the transformation of the integral equation to the differential eguation could be abondoned and a direct numerical solution of the integral equation could be attempted. The direct numerical solution of the integral equation results in a full and nonsymmetric coefficient matrix, increasing the computer memory requirements. This increase was the reason for prefering the conversion to the differential equation in the past. But with the dramatic developments in the computer memory, this increase posseses no serious drawback at present. Nevertheles, old software adopting the ` convert to differantial equation approach ` is stili used in the solution of some thermalization problems. The more rigorous approach involves the direct solution of theneutron transport equation for the unit celi. İn this apprach the real unit celi is cylindricalised using the well-known VVigner - Seitz approximation. Either perfect - reflaction ör white boundary conditions are used at the outer boundary. The transport calculation could be based either on the integro - differential o r integral forms of the transport equation. Solutions based on the integro - differantial eguation utilize mostly the discrete ordinates (SN) technique. But as the number of ordinates increase, the discrete - ordinates solution become more costly. Due to this reason, the integral form of neutron transport equation is preferred by manyworkers for hetoregoneus thermalization calculations. Application of the method of collision probabilities to the integral transport equation seems a very suitable approach for this purpose. This method of solution has also same drawbacks. For öne thing, the scattering is limited to be isotropic in the laboratory system. For another, the calculation of the collision IV.probabilities is a very time intensive process. Especially if the number of regions is taken to be large, the evaluation of collision probabilities may take most of the computer time. The usual flat - flux assumption inherent in the definition of collision probabilities could also be a source of error. But there is a superiority of the method of collision probabilities över the discrete ordinates approach. The number of unknowns is decreased, albeit at the expense of a full and non -symmetric coefficent matrix. The predecessor of the the programs using the collision probability approach in thermalization is the well-known code, THERMOS. THERMOS utilizes an iterative technique for the solution of the linear system. But with the advances in computer resources, a direct solution of the resultant linear system is not a majör problem now. in this work, the determination of the thermal group constants for a light ör heavy water unit celi is the majör objective. The integral transport approach based on the collision probability method is adopted. The number of regions is limited to two, the fuel and the moderator regions, to limit lengthy collision - probability calculations. The scattering model we utilize uses Nelkin' s kemel for hydrogen and deuterium in light and heavy water reactors respectively. Free gas kernel is used to take the scatterings by oxygeninto account. Fuel uranium thermalisition could also be treated by using the free gas kemel. The spectral discretization is accomplished using speed-groups. A library of microscopic crosssections containing the more common isotopes is embeddedwithin the program. The evaluation of the collision probabilities iscarried out by numerical integration of Bickley functions. Clenshaw algorithim is utilized for the computation of the Bickley functions. The resulting linear system after spatial and energy discretization has a full, nonsymmetric structure. The classicalGaussian elimination method is used for the solution of the linear system. The slowing down source is evaluated by assuming a constant 1/E epitermal flux. But the temperature differance between the fuel and the moderetor is taken into consideration. The nuclei included in the internal library include hydrogen, deuterium, graphite, oxygen, aluminum, stainless steel V.dysporsium, luthencium, uranium 235 and uranium 238. The scattering and cross sections are given at 40 speed - points for H, D, U235 and U238. The absorption and fission cross sections of U235 is given at 120 speed- points. The results are compared with the results of another thermalization program previously developed, THERM. This program solves the infinite homogenious medium neutron continuity equation using Nelkin's kernel for hydrogen and deuterium and free gas kernel for oxygen. The heterogenous effects are taken into account by the Annouyal - Benoit- Horrowitz (ABH) technique. The programs are written in the FORTRAN language and and compiled and executed under both MS - DOS and LlNUX operating systems on personel computers with the PENTIUM processor. The program devoleped is called THERMP1U and written in FORTRAN language. The program is run for various water reactor unit cell problems. The thermal group homogenized parameters are calculated, along with the disadvantage factor. The results are compared with results of other programs, namely THERM, which utilizes a homogenous infinite medium calculation and ABH disadvantage factors. The effect of the moderator to fuel ratio on the disadvantage factor is also assessed. The effect of fuel oxygen and uranium thermalization on the thermal group constants are also assessed. The program is restricted to two - region cells.Hence,at its present state, the cladding region can not be treated rigorously. Hence, the program should be extended to include more than two regions. In that case, the cell could be divided into more regions and the flat flux assumption inherent in the calculation of collision probabilities could be relaxed. Also the inclusion of the zirconium hydride kernel is recommended for further work. If this is accomplished, Triga reactor thermalization calculations could be carried out. If the program could be merged with the fast spectrum program, SPEC, developed a, previously at the Institude, the slowing down sources from the epithermal region could be more VIrealistically calculated. Also a joined SPEC - THERMP code would make full spectrum calculations possible, utilizing ` at home` developed programs only. In that case, the extension of the isotops included in the libraries of both programs would be desireble to render a greater variety of spectrum calculations possible. VII