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Yakın Geçmişteki Nükleer Reaktör Dinamik Analiz Yöntemlerine Bir Bakış

Yakın Geçmişteki Nükleer Reaktör Dinamik Analiz Yöntemlerine Bir Bakış

##### Dosyalar

##### Tarih

1996-05-27

##### Yazarlar

Algül, Murat

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Enerji Enstitüsü

Energy Institute

Energy Institute

##### Özet

Bu çalışmada reaktör dinamiği hesaplamalarında geliştirilmiş olan yöntemleri incelemeyi amaçladık. Bu amaç doğrultusunda çeşitli araştırmalar yaparak geliştirilen yöntemleri bulduk. Bu yöntemler arasında kontrol çubuklarının reaktivite değerlerinin ölçülmesi için yapılan çalışmalar, dik-integrasyon yöntemi akılarının açılımı ile çözüm yapan bilgisayar programlarının yapılan, bir-boyutlu çok-gruplu difüzyon denklemlerinin çözümünde geliştirilen metotlar ve üç-boyutlu çok-gruplu akıların hesaplanmasında geliştirilmiş olan programlar ve metotlar bulunmaktadır. Bu yüzden bu çalışmadan son yıllarda geliştirilmiş olan yöntemler ve programlar hakkında bilgi edinilebilir.

In our study we have examined recently improved techniques of nuclear dynamics analyses. We divided these improved techniques to four different groups. Names of groups are reactivity worth of control rods, calculating by expanding the transverse-integrated fluxes, calculation of one-dimensional two or multigroup diffusion equations, and calculations of three-dimensional multi-group fluxes. In one study made for measurement of reactivity worth of control rods, a new method had been improved to determine the safety rod reactivity worth p(t) obtaining rod-drop position-time function z(t). To measure this z(t) function had been used a digital displacement transducer and a dijital optical incremental encoder (DOIE) connected to a serial communication port of a personel computer (PC). In the other one, a method to reduce the dependence on dedector location had been developed for measurement of reactivities of control rods. The rod-drop technique had been used in this method. The transient had been started in an initially critical steady reactor by the sudden insertion of a control rod with worth p0 in a time interval Ate which is insertion time for control rods. This new method had been improved to obtain p0 by using the point reactor model (PRM). In this method, an estimate pom is obtained from the fitting of the deleyed transient, using an adjustment function and considering spatial effects. At the end from made calculations, it had been found that this method does not depend on the relative location of dedectors and control rods, as the method based on the point reactor model does. SPANDEX is a transient nodal expansion method diffusion theory code, employing a nonlinear algorithm and a fifth-order polynomial expansion of the transverse-integrated fluxes. The time integration scheme in this code is a fourth- order implicit generalized Runge-Kutta method with on-line truncation error control and automatic time step selection. Including a robust variable time-step algorithm is important. To show this, a variation of the LMW-light water reactor (LWR) rod motion transient without thermal-hydraulic feedback was constructed. The results of this variation had been obtained, using SPANDEX ' s variable time-step scheme and fixed time-step scheme. From these results, it had been obtained that the variable time-step cases agree with the reference to within 1%, whereas the fixed time-step cases with At=0. 1 s and At=0.25 s over-predict energy production by 2.7 and 9.9%. Transient analysis capability had been added to the advenced nodal methodology of SIMULATE-3. SIMULATE-3 ' s this kinetics capability had coupled the QPANDA advanced nodal methodology with a thermal-hydraulic feedback module. The QPANDA advanced nodal method expands the transverse-integrated two-group nodal neutron fluxes either in a fourth-order polynomial or by using the analytical solution to the diffusion equation in the thermal group. The delayed neutron precursor equations had been solved in six groups by assuming a linear variation in nodal flux over each time step. The required nuclear feedback and kinetics parametres had been obtained and directly from a standard SIMULATE-3 nuclear data library and each simulation had been performed at the true state of exposure for any cycle. The thermal-hydraulic model had been used a one- dimensional, three-equation (mass, momentum, energy) formulation for coolant advection. The accuracy of the code had been assessed by using several benchmark problems, including the LMW benchmark and the Nuclear Energy Agency Committee on Reactor Physics (NEACRP) pressurized water reactor (PWR) rod ejection benchmarks. It had been seen that the results obtained from SIMULATE-3 are in good agreement and that the largest deviation (19%) is in the maximum core power following a seven-decade-increase in power resulting from the hot-zero-power (HZP) rod ejection. VUl The orthogonal collocation method (OCOFE) had been used to solve a one- dimensional multigroup time-dependent diffusion equation. In particular, this method had been developed for the one-dimensional group diffusion and precursor concentration equations in the slab, cylindirical and spherical geometries. In order to apply the orthogonal collocation method, the region had been divided into different elements (k=l,2,...,K) and each element has width hk, where hk=Xk+i-Xk. The group neutron flux and precursor concentration are written at certain collocation points. These collocation points are the roots of Legendre polynomials. In each element, there are a total of N+2 collocation points. N being the internal collocation points. Adding the interface and boundary conditions, a set of equations had been obtained for the global case. The one-dimensional multigroup time-dependent diffusion and the precursor concentration equations are written for each element. The relations in the diffusion equation and the precursor concentration equations written for each element had constructed the basis of the orthogonal collocation method. In order to deal with the time variable, these equations (the diffusion equation and the precursor concentration equations written for each element) are considered for a given time step. In each time step, an eigenvalue is found from an iterative scheme which is then followed by the determination of the group neutron fluxes and the precursor concentrations. The calculated values are then used as input for the subsequent time step and in this way the process continues. On the basis of the orthogonal collocation theory, a computer code had been written in QuickBASIC. The code can be run as a static mode or a dynamic one. Two different sample problems had been used to test the accuracy of the code. The first sample problem is the one-dimensional version of the ANL (Argonne National Laboratory) benchmark problem. The second sample problem used is a two-group time-dependent problem with six groups of delayed neutrons. The results obtained from two sample problems had showed that the orthogonal collocation method is satisfactory. New core-reflector boundary conditions for transient nodal reactor calculations had been developed. These developed new core-reflector boundary conditions are the relations between the nodal face-averaged net current and flux at the core-reflector interfaces. The transverse-integrated one-dimensional two-group IX diffusion equation in the reflector had been used to derive these relations. Solving this equation is not easy in general situation because of the presence of the temporal derivative term and the a priori unknown transverse leakage term L^,(u,t). Therefore, the transient core-reflector boundary condition for slab reflector had been obtained by using the spatially flat frequency approximation and the exponential transverse leakage approximation. For the purpose of applying these approximations, it had been considered that a two-group flux distribution in a semi-infinitive homogeneous slab reflector that is subjected to time-varying x-directed incoming neutrons on one face. Two-group distribution §T (x,t) had been found from the time-dependent two-group diffusion theory model without the transverse leakage. It had been observed that the temporal flux behaviour in the semi-infinitive slab is characterized by the spatially flat frequency Wg(t) and that the spatial flux distribution shows exsponential attenuation coefficient. This observation had been led to the spatially flat frequency approximation for the temporal behaviour of two-group flux in the reflector. As for the transverse leakage, it had been assumed that theL^,(u,t) is proportional to $T (x,t). This assumption had been led to the exponential transverse leakage approximation for L*,(u,t). Core-reflector boundary conditions had been obtained for the L-shaped that faces the core on two faces too like this. To examine the effectiveness of new core-reflector boundary conditions in transient nodal reactor computations, nodal expansion method (NEM) computations with and without explicit representation of the reflector had been performed for Laboratorium fur Reaktorregelung und Anlagen (LRA) boiling water reactor (BWR) and Nuclear Energy Agency Committee on Reactor Physics (NEACRP) pressurized water reactor (PWR) rod ejection kinetics benchmark problems. It had been seen that these new core-reflector produce a significant CPU time saving. A new method to solve one-dimensional time dependent multi-group diffusion equations had been improved using multi-point kinetics equations of the coupled reactor theory. The usual improved quasi-static method had been generalized such that the fission sources for each core or node obtained from multi-point kinetics equations are used as amlitude functions for each node instead of a single amplitude function. Coupling coefficients between nodes had been found that the solution for a benchmark problem was in good agreement with reference solutions. It had been showed that weakly coupled reactors of two cores can be well treated by a two-point model with constant coupling coefficient. In order to perform more sophisticated transient analyses, Siemens has coupled the nodal core simulater PANBOX2 with the plant analysis code RELAP5/MODE2. This coupling had been produced more accurate results, but calculation time had been become very long due to the comlexity of calculating three- dimensional multigroup fluxes. Therefore, to reduce calculation time, an adaptive two-level algorithm for the coupled PANBOX2/RELAP5 system had been developed. The reactor dynamics program system PANBOX is a coupled neutronics and thermal hydraulics code system for the analysis of space-time effects in pressurized water reactors. PANBOX is used for reload safety analysis and all kinds of transient in which the power distirbution is significantly affected. Apart from input and output processors it consists of dedicated modules which treat specific transients such as long-term events like xenon redistribution and short-term accidents like rod ejections. The global solution is combined with an accurate and efficient pin power reconstruction module. Thus the system is capable not only of performing global neutronic/thermal-hydraulic calculations but also of evaluating important safety- related parameters, such as deperture from nucleate boiling ratios and centreline fuel temperatures. The continuing progress in computer technology, characterized by the ever- increasing calculational speed of various computer architectures, had been enabled the direct coupling of up to recently seperate code systems. As a consequnce different areas of analysis like reactor physics, core thermal hydraulics, and plant dynamics can be integrated to increase the accuracy of simulation over that obtained from imposing conservative boundary conditions at the interfaces. Thus, coupling of PANBOX and RELAP5 had been come true and the methods in coupling of PANBOX and RELAP5 had been showed. XI The NESTLE nodal kinetics code had been developed for utilization as a stand-alone code for steady-state and transient reactor neutronic analysis and for incorporation into system transient codes, such as TRAC and RELAP. NESTLE solves the few-group neutron diffusion equation utilizing the nodal expansion method (NEM). Either two or four energy groups may be employed, with full upscattering permitted. Both cartezien and hexagonal geometries are accommodated. The nonlinear iterative method developed by Smith had been used to solve the coupled NEM equations. An adaptive time-step size control method for the neutron kinetics equations had been developed. Neutron kinetics codes utilize the first derivative of the flux, either obsolute or relative, to control the time-step size. Mathematically it is more rigorous to utilize the second derivative of the flux when an Euler backward finite difference is used to discretize the time, implying a second-order truncation error. Performance of the method had been assessed utilizing the NESTLE nodal diffusion theory code.

In our study we have examined recently improved techniques of nuclear dynamics analyses. We divided these improved techniques to four different groups. Names of groups are reactivity worth of control rods, calculating by expanding the transverse-integrated fluxes, calculation of one-dimensional two or multigroup diffusion equations, and calculations of three-dimensional multi-group fluxes. In one study made for measurement of reactivity worth of control rods, a new method had been improved to determine the safety rod reactivity worth p(t) obtaining rod-drop position-time function z(t). To measure this z(t) function had been used a digital displacement transducer and a dijital optical incremental encoder (DOIE) connected to a serial communication port of a personel computer (PC). In the other one, a method to reduce the dependence on dedector location had been developed for measurement of reactivities of control rods. The rod-drop technique had been used in this method. The transient had been started in an initially critical steady reactor by the sudden insertion of a control rod with worth p0 in a time interval Ate which is insertion time for control rods. This new method had been improved to obtain p0 by using the point reactor model (PRM). In this method, an estimate pom is obtained from the fitting of the deleyed transient, using an adjustment function and considering spatial effects. At the end from made calculations, it had been found that this method does not depend on the relative location of dedectors and control rods, as the method based on the point reactor model does. SPANDEX is a transient nodal expansion method diffusion theory code, employing a nonlinear algorithm and a fifth-order polynomial expansion of the transverse-integrated fluxes. The time integration scheme in this code is a fourth- order implicit generalized Runge-Kutta method with on-line truncation error control and automatic time step selection. Including a robust variable time-step algorithm is important. To show this, a variation of the LMW-light water reactor (LWR) rod motion transient without thermal-hydraulic feedback was constructed. The results of this variation had been obtained, using SPANDEX ' s variable time-step scheme and fixed time-step scheme. From these results, it had been obtained that the variable time-step cases agree with the reference to within 1%, whereas the fixed time-step cases with At=0. 1 s and At=0.25 s over-predict energy production by 2.7 and 9.9%. Transient analysis capability had been added to the advenced nodal methodology of SIMULATE-3. SIMULATE-3 ' s this kinetics capability had coupled the QPANDA advanced nodal methodology with a thermal-hydraulic feedback module. The QPANDA advanced nodal method expands the transverse-integrated two-group nodal neutron fluxes either in a fourth-order polynomial or by using the analytical solution to the diffusion equation in the thermal group. The delayed neutron precursor equations had been solved in six groups by assuming a linear variation in nodal flux over each time step. The required nuclear feedback and kinetics parametres had been obtained and directly from a standard SIMULATE-3 nuclear data library and each simulation had been performed at the true state of exposure for any cycle. The thermal-hydraulic model had been used a one- dimensional, three-equation (mass, momentum, energy) formulation for coolant advection. The accuracy of the code had been assessed by using several benchmark problems, including the LMW benchmark and the Nuclear Energy Agency Committee on Reactor Physics (NEACRP) pressurized water reactor (PWR) rod ejection benchmarks. It had been seen that the results obtained from SIMULATE-3 are in good agreement and that the largest deviation (19%) is in the maximum core power following a seven-decade-increase in power resulting from the hot-zero-power (HZP) rod ejection. VUl The orthogonal collocation method (OCOFE) had been used to solve a one- dimensional multigroup time-dependent diffusion equation. In particular, this method had been developed for the one-dimensional group diffusion and precursor concentration equations in the slab, cylindirical and spherical geometries. In order to apply the orthogonal collocation method, the region had been divided into different elements (k=l,2,...,K) and each element has width hk, where hk=Xk+i-Xk. The group neutron flux and precursor concentration are written at certain collocation points. These collocation points are the roots of Legendre polynomials. In each element, there are a total of N+2 collocation points. N being the internal collocation points. Adding the interface and boundary conditions, a set of equations had been obtained for the global case. The one-dimensional multigroup time-dependent diffusion and the precursor concentration equations are written for each element. The relations in the diffusion equation and the precursor concentration equations written for each element had constructed the basis of the orthogonal collocation method. In order to deal with the time variable, these equations (the diffusion equation and the precursor concentration equations written for each element) are considered for a given time step. In each time step, an eigenvalue is found from an iterative scheme which is then followed by the determination of the group neutron fluxes and the precursor concentrations. The calculated values are then used as input for the subsequent time step and in this way the process continues. On the basis of the orthogonal collocation theory, a computer code had been written in QuickBASIC. The code can be run as a static mode or a dynamic one. Two different sample problems had been used to test the accuracy of the code. The first sample problem is the one-dimensional version of the ANL (Argonne National Laboratory) benchmark problem. The second sample problem used is a two-group time-dependent problem with six groups of delayed neutrons. The results obtained from two sample problems had showed that the orthogonal collocation method is satisfactory. New core-reflector boundary conditions for transient nodal reactor calculations had been developed. These developed new core-reflector boundary conditions are the relations between the nodal face-averaged net current and flux at the core-reflector interfaces. The transverse-integrated one-dimensional two-group IX diffusion equation in the reflector had been used to derive these relations. Solving this equation is not easy in general situation because of the presence of the temporal derivative term and the a priori unknown transverse leakage term L^,(u,t). Therefore, the transient core-reflector boundary condition for slab reflector had been obtained by using the spatially flat frequency approximation and the exponential transverse leakage approximation. For the purpose of applying these approximations, it had been considered that a two-group flux distribution in a semi-infinitive homogeneous slab reflector that is subjected to time-varying x-directed incoming neutrons on one face. Two-group distribution §T (x,t) had been found from the time-dependent two-group diffusion theory model without the transverse leakage. It had been observed that the temporal flux behaviour in the semi-infinitive slab is characterized by the spatially flat frequency Wg(t) and that the spatial flux distribution shows exsponential attenuation coefficient. This observation had been led to the spatially flat frequency approximation for the temporal behaviour of two-group flux in the reflector. As for the transverse leakage, it had been assumed that theL^,(u,t) is proportional to $T (x,t). This assumption had been led to the exponential transverse leakage approximation for L*,(u,t). Core-reflector boundary conditions had been obtained for the L-shaped that faces the core on two faces too like this. To examine the effectiveness of new core-reflector boundary conditions in transient nodal reactor computations, nodal expansion method (NEM) computations with and without explicit representation of the reflector had been performed for Laboratorium fur Reaktorregelung und Anlagen (LRA) boiling water reactor (BWR) and Nuclear Energy Agency Committee on Reactor Physics (NEACRP) pressurized water reactor (PWR) rod ejection kinetics benchmark problems. It had been seen that these new core-reflector produce a significant CPU time saving. A new method to solve one-dimensional time dependent multi-group diffusion equations had been improved using multi-point kinetics equations of the coupled reactor theory. The usual improved quasi-static method had been generalized such that the fission sources for each core or node obtained from multi-point kinetics equations are used as amlitude functions for each node instead of a single amplitude function. Coupling coefficients between nodes had been found that the solution for a benchmark problem was in good agreement with reference solutions. It had been showed that weakly coupled reactors of two cores can be well treated by a two-point model with constant coupling coefficient. In order to perform more sophisticated transient analyses, Siemens has coupled the nodal core simulater PANBOX2 with the plant analysis code RELAP5/MODE2. This coupling had been produced more accurate results, but calculation time had been become very long due to the comlexity of calculating three- dimensional multigroup fluxes. Therefore, to reduce calculation time, an adaptive two-level algorithm for the coupled PANBOX2/RELAP5 system had been developed. The reactor dynamics program system PANBOX is a coupled neutronics and thermal hydraulics code system for the analysis of space-time effects in pressurized water reactors. PANBOX is used for reload safety analysis and all kinds of transient in which the power distirbution is significantly affected. Apart from input and output processors it consists of dedicated modules which treat specific transients such as long-term events like xenon redistribution and short-term accidents like rod ejections. The global solution is combined with an accurate and efficient pin power reconstruction module. Thus the system is capable not only of performing global neutronic/thermal-hydraulic calculations but also of evaluating important safety- related parameters, such as deperture from nucleate boiling ratios and centreline fuel temperatures. The continuing progress in computer technology, characterized by the ever- increasing calculational speed of various computer architectures, had been enabled the direct coupling of up to recently seperate code systems. As a consequnce different areas of analysis like reactor physics, core thermal hydraulics, and plant dynamics can be integrated to increase the accuracy of simulation over that obtained from imposing conservative boundary conditions at the interfaces. Thus, coupling of PANBOX and RELAP5 had been come true and the methods in coupling of PANBOX and RELAP5 had been showed. XI The NESTLE nodal kinetics code had been developed for utilization as a stand-alone code for steady-state and transient reactor neutronic analysis and for incorporation into system transient codes, such as TRAC and RELAP. NESTLE solves the few-group neutron diffusion equation utilizing the nodal expansion method (NEM). Either two or four energy groups may be employed, with full upscattering permitted. Both cartezien and hexagonal geometries are accommodated. The nonlinear iterative method developed by Smith had been used to solve the coupled NEM equations. An adaptive time-step size control method for the neutron kinetics equations had been developed. Neutron kinetics codes utilize the first derivative of the flux, either obsolute or relative, to control the time-step size. Mathematically it is more rigorous to utilize the second derivative of the flux when an Euler backward finite difference is used to discretize the time, implying a second-order truncation error. Performance of the method had been assessed utilizing the NESTLE nodal diffusion theory code.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Enerji Enstitüsü, 1996

Thesis (M.Sc.) -- İstanbul Technical University, Energy Institute, 1996

Thesis (M.Sc.) -- İstanbul Technical University, Energy Institute, 1996

##### Anahtar kelimeler

Dinamik analiz,
Nükleer reaktörler,
Dynamic analysis,
Nuclear reactors