HOMOGENIZED CROSS SECTION DETERMINATION USING MONTE CARLO SIMULATION by ILKER TARI B.S., Hacettepe University, Turkey 1987) M.S. University of Michigan 1991) Submitted to the Department of Nuclear Engineering in Partial Fulfillment of the Requirements for the Degree of NUCLEAR ENGINEER and the Degree of MASTER OF SCIENCE at the MASSACHUSETTS INST111M OF TECHNOLOGY January 1994 0 Ilker Tari, 1994. All rights reserved. The author hereby grants to MIT and Turkish Ministry of Education permission to reproduce and distribute copies of this thesis document in whole or in part. Signature of Author Department of Nuclear Engineering January 28, 1994 Certified by Allan F. Henry Professor of Nuclear Engineering Thesis Supervisor Accepted by Allan F. Henry MASSACHLISETT:: WSTITU -iE PIT APR 26 1994 i-loriAWES cience Chairman, Department Committee on Graduate Students HOMOGENIZED CROSS SECTION DETERMINATION USING MONTE CARLO SIMULATION by ILKER TARI Submitted to the Department of Nuclear Engineering on January 28, 1994, in partial fulfillment of the requirements for the degrees of NUCLEAR ENGINEER and MASTER OF SCIENCE ABSTRACT This thesis is an application of Monte Carlo simulation techniques to homogenized cross section determination. MCNP Monte Carlo code was used for obtaining homogenized node cross sections for QUARTZ triangular-z nodal code model of MITR-II (MIT research reactor). According to specifically developed original scheme, three different MCNP models of MITR-11were generated.'These models were used in several MCNP runs to obtain cell fluxes and reaction rates. These results were processed using a homogenization scheme to generate homogenized total, absorption, fission and elastic scattering cross sections and diffusion coefficients for two energy groups. The accuracy of the specifically developed cross section processing programs were tested. Axial and radial distributions of the results were investigated. The general accuracy of the procedure was evaluated and possible sources of error were identified. A simple problem which is a portion of a MITR-11 fuel element was modeled and used for demonstrating the suggested one-MCNP-run procedure. 'Me computer facility requirements were evaluated and some projections about the future requirements were discussed. Three major outcomes of this thesis are : () threenew MCNP models of MITR-II, 2) two group reaction rate and flux data for every cell represented in the MCNP model of MITR-H homogenized cross sections for two groups. Thesis Supervisor- Prof. Allan F. Henry Thesis Reader: Prof. David D. Lanning 2 3 Triangular-z nodal TABLE OF CONTENTS Page ABSTRACT 2 TABLE OF CONTENTS 3 LIST OF FIGURES AND TABLES 4 CHAPTER I INTRODUCTION 6 1.1. THESIS OBJECTIVE 6 1.2 BACKGROUND ON MITR-H 7 1.3 A BRIEF BACKGROUND OF MONTE CARLO SMULATION AND MCNP 12 1.4 BACKGROUND ON QUARTZ NODAL CODE 13 1.5. ORGANIZATION OF THE THESIS 15 CHAPTER 2 PROBLEM, SOLUTION STRATEGY AND MCNP MODELS 16 2. 1. WHY MCNP ? 16 2.2. GENERAL STRATEGY AND PROCEDURE 19 2.2.1. QUARTZ Model of M1717R-II 19 2.2.2. Organization and Distribution of the Tasks 21 2.3. MCNP MODELS AND THEIR EVOLUITON 24 2.3.1. Original Model 24 2.3.2. Simplified Model 24 2.3.3. Triangulated Model 32 2.3.4 13 Symmetry Incore Fully Triangulated Model 35 CHAPTER 3 PRE-PROCESSING, PROCESSING AND POST-PROCESSING 38 3. I. MCNP INPUT PREPARATION AND PRE-PROCESSING PROGRAMS 38 3..1. 1. Tally Cards 38 3.1.2. Stochastic Volume Calculation by using MCNP 38 3.1.3. Segmentation 39 3.2. MCNP RUNS FOR OBTAINING CELL FLUXES AND REACTION RATES 39 3.3. THE HOMOGENIZATION SCHEME AND POST-PROCESSING PROGRAMS 41 3.3.1. Homogenization Scheme 41 3.3.2. Calculation of the Statistical Erors 42 CHAPTER 4 RESULTS 43 4.1. INCORE RESULTS 44 4.2. OUT OF THE CORE RESULTS 44 4.2. I. Results for the Nodes Above the Bottom Level of The Fuel 44 4.2.2. Results for the Nodes Below the Bottom Level of ne Fuel 47 3 4.3. SURFACE FLUX AND SURFACE CURRENT RESULTS 47 4.4. GROUP TO GROUP SCATTERING 47 4.5. NEUTRON BALANCE 50 4.6. GENERAL TRENDS OF THE CROSS SECTION RESULTS 51 CHAPTER CONCLUSION 67 5.1. GENERAL EVALUATION OF THE RESULTS 67 5.2. COMPUTER FACILITY REQUIREMENTS 69 51.1. Required Memory for MCNP runs 69 5.2.2. Relation between CPU Time and the Number of Cells in the Model 70 5.2.3. Relation between CPU Time and the Tallies in the Model 71 5.2.4 Sorage Space Requirement 71 5.3. CONT'RIBLMONS 71 5.4. RECOMMENDATIONS FOR THE FUTURE WORK 72 REFERENCES 73 APPENDIX A INPUT TALLY CARDS 74 APPENDIX 87 PROCESSING PROGRAMS APPENDIX C SAMPLE CROSS SECTION RESULTS 112 APPENDIX D ONE GROUP NODE BALANCE CHECK RESULTS 131 APPENDIX E THE M T OF HOMOGENICZATIONPROCEDURE 136 LIST OF FIGURES AND TABLES Page Figure 11. Artist's rendering of M[TR-H reactor facility 8 Figure 12. N= 9 -11fuel element with its dimensions Figure 13. MITR-H cote number 2 loading with dummy and 22 fuel elements 10 Figure 14. Scaled x-y view of MITR-II with reflectors II Figure 1.5. QUARTZ triangular 14 mesh geometry Figure 2.1.Azimutal enlarged CITATION model of MITR-11 17 Figure 22. The 3-D representation of QUARTZ model of M1TR-II 20 Figure 23. Tix oganization of the tasks in the development of MCNP model 22 Figure 24. The tasks after the model was generated 23 Figure 25. Original Model of MITR-11(y-z view) 25 Figure 26. Original Model of MITR-II (x-y view) 26 Table 2 1 'Me comparison of CPU time and k-effective results for different runs of two models 27 Figure 27. One of the bottom detectors in guide tube 29 4 Figure 28. Simplified Model before graphite reflector changed to hexagonal prism (x-y view) 30 Figure 29. Simplified Model after graphite reflector changed to hexagonal prism (y-z view) 3 Figure 210. Triangulated Model (x-y view) 33 Figure 21 1. Triangulated Model (y-z view) 34 Figure 212 'Me 13 symmetry boundaries 36 Figure 213. The 13 symmetry triangulated core model (x-y view) 37 Table 3 1 'Me comparison of CPU time and k-effective results for MCNP tally runs 40 Figure 41. 2-D nodal map of QUARTZ model showing the I and J indices 45 Table 4 1. The smple results for the radial distribution of the cross sections and flux 46 Table 42. Axial distribution of flux and cross sections for triangular node 1=I 1, J= 1 48 Table 43. Axial distribution of flux and cross sections for triangular node 1=17,J=7 49 Figure 42. Radial flux distributions 52 Figure 43. Radial distributions of homogenized croaa.sections 53 Figure 44. Radial distribution of statistical errors 54 Figure 45. The axial distribution of fluxes for the 2 energy groups in node 17,7) 55 Figure 46. The axial distribution of homogenized cross section results in node 17,7) 56 Figure 47 'Me axial distribution of statistical error for the 2 energy groups in node 17,7) 57 Figure 48. MCNP axial thermal flux distribution for Aluminum of A-3 60 Figure 49. MCNP axial fast flux distribution for Aluminum of A-3 61 Figure 410. MCNP axial thermal flux distribution for Plate I of B-7 62 Figure 41 1. MCNP axial fast flux distribution for Plate 63 of B -7 Figure 412. MCNP axial thermal flux distribution for Pate 15 of B-7 64 Figure 413. MCNP axial fast flux distribution for Plate 15 of B-7 65 Table 5. 1. Summary of the data relevant to the computing resources 69 5 CHAPTER INTRODUCTION 1.1. THESIS OBJECTIVE This thesis is an integrated part of the department wide effort to obtain tools for real time transient analysis of nuclear rectors. The real time determination of spatial power distribution in the core and the total core reactivity is the key issue to improve the safety and control of the nuclear reactors. 'Me real time calculations and analysis requires accurate and faster methods to determine reactor physics parameters. The theoretical, and experimental nodal synthesis methods are the promising candidates for this task. Recently a quadratic nodal code for triangular-z geometry QUARTZ) is developed by T.F. DeLorey [D-1] and tested against several static and transient benchmark cases. Application of QUARTZ to calculation of a real reactor for the first time, requires homogenized cross section data for every node in its defined mesh. The thesis project of W.S. Kuo [K-1] involves this kind of application of QUARTZ to Massachusetts Institute of Technology Research Reactor (MITR-H), therefore the homogenized cross sections for triangular-z mesh model of MITR-11 for QUARTZ are required. The main objective of this thesis is to generate the required cross section data by using a Monte Carlo simulation. The MCNP Monte Carlo code developed at the Los Alamos National Laboratory is chosen for this job, it being the only readily available code that can provide enough flexibility to obtain satisfactory results. Some unique characteristics of the MITR-Il makes reactor analysis impossible without using a Monte Carlo simulation. During the course of this thesis work, a consistent and original approach was developed by the author and Kuo. Since the application of the procedure by one person was impossible to complete within the time limitations, the task was divided between the author and Kuo. The task division and the approach will be discussed-in the next chapter. Sections 12 through 14 briefly describe MITR-Il, MCNP and QUARTZ for the unfamiliar reader. More detail about MITR-II and MCNP is presented as required for the understanding of the related topics. For more information on those topics, references [M-11 and [B-1] are very good sources of information for MITR-H and MCNP, respectively. 6 1.2. BACKGROUND MITR-11 is a ON MITR-11 MWth research reactor at the Massachusetts Institute of Technology which has been in operation since 1975. It serves as an interdepartmental research and education facility. It is a unique design created by MIT Nuclear Engineering Department students, faculty and staff. Figure 11 shows the general view of the entire reactor and the associated research facilities. MITR-II has a very compact core design involving 27 rhomboid assembly locations. These locations can be filled with fuel assemblies, A6061 dummy elements or with special experimental apparatus. Each fuel element consists of 15 highly enriched (-93% U-235) UAIxfuel plates as shown along with dimensions in Figure 12 The Core elements form three separate rings with some parts of the core divided by boron inserts. Figure 13 shows the MITR-H fresh Core-2 loading arrangement with dummy elements and 22 fuel assemblies. This is the case for which the homogenized cross sections will be obtained. In this case, the A-ring consists of two y elements and a fuel element occupying the small hexagonal section in the middle of the core. The B-ring is a hexagonal ring surrounding the A-ring. It includes 3 dummy and 6 fuel elements. Ile A-ring and B-ring are divided by a hexagonal structure called a spider which is partly Aluminum, partly water, and some parts of which include boron inserts. The outer ring which includes 5 fuel elements is called as the C-ring. Some elements in 13-ringand C-ring are separated by 3 other structures called arms, and some parts of these ams include boron inserts. The reactor core is surrounded by a hexagonal Aluminum structure in which the control blades, water holes and regulating rod are nested. 'Me six boron control blades are located at the edges of the hexagon. Each comer of the hexagon has a cylindrical hole called a water hole or water vent hole. 'Me main function of the water holes is the ventilation of the water replaced by control blades during the control blade insertion. 'Me water hole on the right corner in Figure 13 includes the regulating rod which uses Cadmium as a control material and functions as a mechanism for fine reactivity adjustments and flux shape regulation. All constituents of the core are numbered starting rom the position of the regulating rod and numbering in a clockwise dection. For example A-1 is the fuel element in the A-ring nearest the regulating rod where is in water hole 1. MITR-11 core is cooled with light water. 'Me core tank which holds the core itself and the coolant, is placed in another tank fled with heavy water which acts as both moderator and reflector. The reflector tank is also surrounded by an approximately 60 cm thick graphite reflector. As can be seen from Figure 14, MITR-II core is a very compact design and is neutronically highly coupled. The MITR-II facility also includes several neutron beam ports, thimbles and pneumatic tubes for both incore and out of core irradiation and a medical therapy facility at the bottom of the reactor. Incore experiments can be conducted by replacing a dummy element with a rhomboid shaped experimental apparatus. 7 (1) LU Q C LL. .j z cc LLJ CL x z z w z 0 0. 2 00 cc 0 cc cc LLI 1-: U. 0 Figure 1.I Artises rendering of N=-II reactor facilitY (ad-Vted ftm [M-21) 8 A-A CROSS SECTION ----i A A A C T I v 56.83-4 cm E F 66 i7 cm n U E L 0.4 cm Figure 12 MITR-11 fuel element with its dimensions 9 10 Absorber Plate RR: Regulating Rod CB: Control Blade WH: Water Hole Figure 13 MrM-II core number 2 loading with 10 dummy and 22 fuel elements C C i -I i L II L C -7 - i I I CD - 0 , Ln I CD 0 I . I. I. . I. . . .I -I - - I- - - I- I- - - -I I---- -I I- I---I I- I I I . . . ... .. .I . . . . . . . . . . . . . . - 100 -50 0 50 Figure 14 Scaled x-y view of MITR-11with reflectors. Ii . . . . . . . . . . 100 . . 1.3 A BRIEF BACKGROUND OF MONTE CARLO SIMULATION AND MCNP Parts of this paragraph are taken directly from the MCNP Manual [B-1]. Monte Carlo methods are very different from deterministic transport methods. Deterministic methods solve the transport equation for the average particle behavior. By contrast, Monte Carlo does not solve an explicit equation, but rather obtains answers by simulating individual particles and recording some aspects (tallies) of their average behavior. The average behavior of particles in the physical system is then inferred (using the central limit theorem) from the average behavior of the simulated particles. The central limit theorem says that for sampling from almost any distribution, the distribution of the smple mean is approximately normal provided the sample size is large enough -1]. Not only are Monte Carlo and deterministic methods very different methods of solving a problem even what constitutes a solution is different. Deterministic methods typically give fairly complete information (for example, flux) throughout the phase space of the problem, whereas Monte Carlo supplies information only about specific tallies requested by the user. Monte Carlo can be used to theoretically duplicate a statistical process (such as the interaction of nuclear particles with materials) and is particularly useful for complex problems that can not be modeled by computer codes of deterministic methods[B-1]. MCNP is a general-purpose, continuous-energy, neutron/photon/electron Monte Carlo =sport generalized-geometry, time-dependent, coupled code. MCNP is widely used and its accuracy has been tested throughout these years of heavy usage. To use the code, the user creates an input file that is subsequently read by MCNP. This file which is referred to as the MCNP model in this thesis, contains information about the problem in areas such as the geometry specification, the description of materials, which crosssection evaluations to use, the location and characteristic of the source, and the type of answers or tallies desired. A more detailed description of MCNP options can be found in User's Manual [B-1] and its supplements [B-2]. Some definition's of the terms used in this thesis related to MCNP are the following. surface and surface definition In MCNP input geometry of the model is defined by using surfaces. MCNP has several surface definition tools that can be used to define fst- and second-degree surfaces and some special fourth-degree surfaces. cell and cell definitigIL Cells are the units that are used to define geometry. They are defined as the volumes bounded by the defined surfaces. 12 tally and LaUYdefinitions as mentioned earlier, MCNP results are obtained by following histories in the defined geometry. Tallies are the statistical results of that procedure and they can only be obtained for defined surfaces and cells. MCNP can tally seven major quantities. The ones used in this project are Fl:surface current, F2:surface flux and F4:track length estimate of cell flux. source definitions and Thecritical MCNP has several source definitions to generate the histories and introduce them to the geometry. 'Me ones used are the surface source and the criticality source. 'Me criticality source runs are the ones that starting with the initial source points, create source points for the next group of initiating particles. Each group of particles is called a cycle, and each cycle is introduced at the source points created by the previous one. One can think of source points as the points where the fission events take place. he criticality run gives as a result the eigenvalue (criticality) of the reactor model. universe-fl1l and =ated structures definitions Some repeated structures in the geometry can be defined easily by using the special options of MCNP introduced in the recent versions of the code. The newest and the most frequently used of these options is the universe-fill scheme. In this scheme several cells-can be defined as a universe and the universe can be used in some other cell definitions with fill command. These filled cells act as windows that the universe viewed from. Detailed descriptions of all these definitions can be found in the manual [B-1]. 1.4. BACKGROUND ON QUARTZ NODAL CODE QUARTZ is a =dratic polynomial Reactor code for 3:nangular-Z geometry developed by DeLorey [D-11. This in-house code solves the quadratic nodal equations using a non-linear iteration scheme, based on the corrected, mesh-centered finite difference equations. These equations are forced to match the quadratic equations by computing discontinuity factors iteratively during the solution [13-I]. QUARTZ uses an equilateral triangle-z geometry. The triangle side length is variable, but the triangle must be equilateral. An example of the nodal mesh geometry of QUARTZ is given in Figure 1.5. his mesh structure is especially suitable to represent the core elements of MITR-II that are rhomboids with equal sides. More information about QUARTZ can be found in references [D-1],[D-2] and [K-1]. 13 TRIANGULARNMESH a 1=1 1=2 I Z-MESH: I K increases from bottom to top I Figure 1.5 QUARTZ triangular-z mesh geometry 14 1.5. ORGANIZATION OF THE THESIS After this introduction chapter, in Chapter 2 the overall problem and the approach used for its solution are discussed with respect to the MCNP models created to obtain the data for homogenization. Chapter 3 gives some information about the pre-processing software written to prepare input data and other data gathering processes. It also discusses the MCNP runs and the homogenization schemes for incore and out of core homogenized cross section calculations, including post-processing procedures and the software written to implement them. In Chapter 4 results are presented and the procedure for using them in QUARTZ is discussed. The large volume of data obtained is summarized to give the general trends in the forms of tables and graphics. The thesis conclude with Chapter discussing the validation of the cross section results and evaluation of the general solution scheme. A discussion of computer facility requirements for this End of job, a summary of the contributions made in this thesis and recommendations for the future work are also given in this chapter. 15 CHAPTER 2 PROBLEM, SOLUTION STRATEGY AND MCNP MODELS 2.1. WHY MCNP ? MCNP is the most suitable Monte Carlo code available for the case at hand, as offered, for example KENO Monte Carlo code which has been tested by Kuo was found unsuitable. New versions of MCNP have enough generality for most reactor physics applications. However, we have found no application of MCNP to homogenized cross section generation in the literature. Although the MCNP manual includes some hints, its application to that area requires creative approaches and sometimes tricks to fake the code. During the course of this work, among some other tricks tried -such as using the surface source read-write option instead of a criticality run for larger numbdr of histories- the approach discussed in the next section is chosen eventually. It seems to be the best approach possible. Most of the commercial and research oriented computer codes were developed for commercial nuclear plants, and therefore generally use Cartesian or r-O-z geometry along wiih fixed geometrical shapes convenient for the representation of BWR and PWR cores. Since the MITR-II core has a very unique geometry, it is impossible to represent it by these codes without major approximations to the geometry. Calculations for reactor operations for the MIIR-II have been done regularly by the reactor staff using the CITATION code [F-1]. But CITATION is in r-O-z geometry which, as seen in Figure 21 does not conform well to the MITR design. On the contrary, MCNP allows the definition of almost any possible geometric shape that can be associated with an open or closed form polynomial function. Such generality is required for a good representation of MrIR-II. 16 AZIMUTHAL MESH: CORE SECTION ENLARGED MODEL M.I.T.Ft.11 Figtwe 21 Azimuthal enlarged CITAMN mdel OfMITR-11 17 MCNP has some other advantages over deterministic transportcodes that can be itemized as • It has the inherent characteristic of a Monte Carlo simulation that the accuracy of the results is not limited by any theoretical approximation. • The continuously-updated, continuous-energy cross section libraries allows calculations to be made without any energy group approximation, and by using the most recent cross section data sets. • The model geometry plotting tool that comes with the package aows the user to check the model at every step of the development process. Most of the figures included in this thesis were generated by using this tool. On the other hand, MCNP has some limitations and inconvenient characteristics The accuracy of MCNP results is limited by the statistical nature of the model. Results can be obtained with any desired statistical certainty, provided that a sufficient number of histories is followed. The larger the number of histories, the better the results, however, also, the longer MCNP runs. Thus to obtain the desired accuracy may be very expensive. MCNP has some variance reduction options for increasing the accuracy without increasing the number of histories. However they are not recommended for the kind of applications associated with this research CB-11. Some other limitations of MCNP are: • MCNP can provide only the reaction rates and fluxes for each defined cell in the model. To obtain cross sections, post processing is required. • Tallying is possible only over the defted cells and surfaces of the model. If the desired cells can not be modeled, the post processing of the data is required. • MCNP does not provide group-to-group scattering reaction rates. Therefore it is impossible to obtain group-to-group scattering cross sections directly from MCNP results. Another reason for the selection of MCNP is the existing MCNP model of MITR core number 2 for which the accuracy has been tested oginally by Redmond [R-2] and by several users including the author [T-11. The model is a very detailed representation of MITR-II with its research facilities including the beam ports and the medical therapy room. Since it was originally developed for more general purposes (in particular for BNCT research), it includes some unnecessary portions of the facility when the primary interest is in the core and reflector area. A more detailed description of this model will be given in Section 23. 1. 18 2.2. GENERAL STRATEGY AND PROCEDURE The major goal of the thesis is to represent the Wmgular-z nodes of the QUARTZ model of MITR-11by an MCNP model and using this MCNP model to obtain required homogenized cross sections for each node of the QUARTZ model. I MCNP calculations raise two major difficulties: long CPU (Central Processing Unit) time, and large computer RAM (Random Access Memory) requirements. These are the major concerns of the present project As mentioned above the MITR-11model of Redmond is geometrically more detailed than required and includes some parts of the reactor that are not of interest for a core-related reactor physics study. Nevertheless it is reasonable to assume as a starting point, that Redmond's model is a good representation of the MITR-11 reactor geometry itself. Its accuracy has been proven several times by both Redmond [R2][R-3], and the author [T-1]. Its geometric complexity is a drawback with respect to CPU time and RAM, but this complexity is the characteristic of the reactor itself and must be kept as it is, to get reliable results. By keeping the iportant parts of the model and changing some definitions to simplify the geometric representation of MITR-H a simplified model was obtained from the original. Taking this simplified model as a basis, a new model consisting of triangular-z cells used for the QUARTZ model of the MITR-11,was developed Mom detailed descriptions of these QUARTZ and MCNP models are given in Section 22.1 and Section 23. 2.2.1. QUARTZ Model of MITR-II The QUARTZ model of MITR-11 includes Oxl6 nodes as shown three-dimensionally in Figure 22 (adapted from reference [K- I]). The 24 nodes in the center represents the core portion of the reactor, and the outer boundary of the graphite is modeled as a hexagonal prism. The number of axial nodes was originally set as 12 sarting from the bottom of the fuel to the top of the fuel. However, initial results showed that a constant albedo boundary condition at the bottom (required by QUARTZ) was not correct because of the D20 reflector effects, a portion of the bottom reflector 4 more axial layers of nodes) was added to the model. The energy group structure was set at 2 groups, one from MeV. 19 to 0625 eV and the other from 0625 eV to 20 z I I 1 ,b i Figure 2.2 The 3-D representation of QUARTZ model of MITR-H. 20 2.2.2. Organization and Distribution of the Tasks As mentioned earlier the project was divided between the author and Kuo as shown in Figure 23 and Figure 2.4. Details of the division of work are given in the next section. Basically, the node-homogenized cross sections and node-averaged fluxes wereobtained by the author, and surface fluxes and currents were obtained by Kuo. Since MCNP does not have the required options to obtain cross section results, the homogenized cross sections were obtained by processing MCNP reaction rates and fluxes by volume-averaging as will be discussed in Section 33. However, surface fluxes and surface currents can be obtained from MCNP results directly. Since to obtain the surface currents and surface fluxes is the easier and less time consuming part of the process, Kuo also obtained the group-to-group scattering cross sections and discontinuity factors for each node by putting together the results from both parts of the process. A more detailed description of the portion of the work executed by Kuo can be found in his thesis [K-11. 2-1 Original Model MITR-H Core-2 I I I rI Remove neutron beam ports and every cell below the bottom of the reflector tank (IT) Small Model I I I I I I I I I I I I Replace graphite reflector with I 30 cm thick cylindrical sel I (M I I I I I Modify cells at the upper part of the core tank and bottom water hole support flanges WSK) I I I I I I I I I Add 9 detectors to water holes Z 4 and 6 according to given specifications by Shelby (IT & WSK) Detector Model I I I L rI I Graphite shape is changed to hexagon (WSK) I I I I I I I - I Separate cells,between top and bottom levels of fuel from the rest of the cells (IT & WSK) I I I I I I I I I Simplified Model I I Triangulated Model I Triangulatethe separatedout of core cells M I I I L I IT: Ilker Tari WSK: Weng-Sheng Kuo Figure 23 The organization of the tasks in the development of M(NP Model 22 Simplified Model A Tally surface currents and surface fluxes after partitioning the tangles with universe-fill (WSK) Tally Reaction rates and cell fluxes M OUT-OF-CORE (ABOVETHE BOTTOM OF FUEL) Triangulated Model Tally control blade ring surface currents and by segmenting the cells physically (WSK) Tally Reaction rates and cell fluxes M. OUT-OF-CURIF, (BELOW THE BOTTOM OE FURL) I TriangulatedModel I Extent triangulation 4 layers below 5 Tally surface currents by segmenting (WSK) Tally Reaction rates and cell fluxes M IT: Ilker Tari, WSK: Weng-Sheng Kuo Figure 24 The tasks after the model was generated. 23 2.3. MCNP MODELS AND THEIR EVOLUTION During the model development stages,.the original model (Redmond's model) which includes features not needed for present purposes was simplified and then tested for consistency against the original model. 'Men from the simplifted model by a tangulation process discussed below, the triangulated model was generated. This final model was used for tallying in different ways by both the author and Kuo A 13 triangulated core model developed for a stochastic volume calculation is also discussed below. 2.3.1. Original Model The Original model as discussed above was developed and tested by Redmond. Details concerning the model and its preparation can be found in references [R-21 and [R-31.The model represents the fresh core-2 with control blades positioned such that the reactor is critical, therefore MCNP runs of the model give k-effective very close to 1.00. The difference if any is a result of statistics and some minor approximations in the model. Figure 25 and Figure 26 shows two different views of the original model. 2.3.2. Simplified Model Since the present research is concerned only with the parts of the reactor included in the QUARTZ model, the original model of MITR-II includes more detail than needed. By making several simplifications and getting rid of the unnecessary prts, the CU time requirement can be reduced. The modifications made were the following: The beam tubes, medical therapy facility and everything below the reflector tank bottom hemisphere were removed. The resultant model is called the Sall Model. This model was tested and the results showed that ftuther simplification was possible. By using this model, the difference between reflective and no-incoming-flux boundary conditions was tested. The results from the several runs to obtain cross sections for assemblies A 1, B 4, C-8 and C- 11 showed that the reflective boundary condition has little effect on the cross section and criticality results, but increases CPU time as compared to the noincoming-flux condition. herefore the boundary condition selected was the no-incoming-flux condition. 24 tTs Figure 25 Original Model of MITR-H (y-z view) 25 Figure 26 Original Model of MUR-11 (x-y view) 26 As a further simplification the bottom hemisphere of the reflector tank was removed and reflector thicimess was reduced by almost half to 30 cm. This model was named the Simplified Graphite Model or simply: Simplified Model. Tests showed that, without loss of accuracy, the CPU time requirement was reduced 30% compared to the original model. Table 21 shows the fdings from criticality runs to obtain fluxes for assemblies C-11, C-8, B-4 and A-1 for 35 cycles of 3000 neutrons and for 205 cycles of 3000 neutrons (no tallies being made for the first cycles). Although the problem is the same in all cases, because of the limitations of the model, a separate run has to be made to edit each individual assembly. 'Me reason for the k-effective difference among the runs for the same model and size is that different source files were used everytime. Model and number of cycles CPU time used of 3000startingparticles (minutes) K-effective Original 35 cyclesfor C-11 322.97 0.98688 Original 35 cyclesfor C-8 320.72 0.99379 Original 35 cyclesfor B-4 325.93 0.99427 Original 35 cyclesfor A-1 329.88 0.99470 Original 205 cycles 1610.36 0.99281 Simplified 35 cycles for C11 204.50 0.99164 Simplified 35 cycles for B-4 209.79 0.99111 Simplified 35 cycles for A - 211.88 0.98593 Simplified 205 cycles 1205.72 0.99094 Simplified 205 cyclesfor WHs 1157.53 0.99338 Table 21 The comparison of CPU time and k-effective results for different runs of two models. 27 The similar eigenvalue and the similar cross section results suggest that the Simplified model is as good as the original model. Using this simplified model, the following cell modifications were made by Kuo: The comer cells of the control blade hexagon (the Al supporting structure where the control blades are located) and the cells in the curvbd part of the upper portion of core tank were homogenized as a mixture of the materials originally modeled. In addition to these modifications the final model includes 9 detectors and paced in the water holes 24 and 6 as suggested by Shelby [S-11. The geometry and material specifications of the detectors were obtained from Shelby's thesis. According to his suggestions, each water hole has 3 detectors axially located in different positions in a guide tube immersed in the water hole. One of the detectors as defined for the model is shown in Figure 27. The specifications for these fission chamber detectors can be found in Shelby's thesis [S-1]. After the addition of the detectors, this model is used for incore runs. For the incore triangular nodes and for out of core nodes, two different paths were followed. For incore nodes, after voiding the repeated sructure procedure, cell reaction rates and fluxes were obtained for each cell in the core hexagon. Since the ells of interest are the fuel plates and water channels making up a rhombic assembly, it is necessary to assume that cross sections found from homogenizing a given fuel with its associated moderator are partially constant, then, when a given rombic element is cut into triangles we can take the cross sections for the portions of a fuel plate belonging to different triangles to be that of the plate itself. The homogenization process is discussed further in Section 33. For out of core nodes another model is created. Figure 2.8 and Figure 2.9 shows two different views of the model after these modifications. 28 i i i I II I I I I 0- I CN I . rl) I I,I- -4 -3 -2 1 0 1 Figure 27 One of the bottom detectors in guide tube 29 2 3 4 f Figure 28 Simplified model before graphite reflector changed to hexagonal prism x-y view) 30 D20 Figure 2.9 Simplified model after graphite reflector changed to hexagonal prism (y-z view) 31 2.3.3. The Triangulated Model As mentioned earlier MCNP can not tally energy group cross sections. Rather it can provide energy group cell fluxes by using 4 tallies and cell reaction rates, again by using F4 along with microscopic cross section and atom, density multipliers. Atom densities can be obtained from the Table 50 of MCNP output and the multiplier indicators for different microscopic cross sections are given in MCNP manual. Thus, by running MCNP, the reaction rates and fluxes for each ell can be obtained, and then by using these data a homogenization process can be applied to get homogenized cross sections for triangles that include MCNP cells. To obtain cross sections for Wangles, they must be defined in the MCNP model. In the Simplified Model, most of the defined cells fall into core hexagon (hexagonal region of 27 elements). 'Mat part of the geometry is the most complicated part. The Simplified Model incore cells are defined by using repeated structures option. This procedure reduces the number of cell definitions very significantly. However for triangulation, the repeated structures need to be removed, and this removal causes the number of cells in the core to increase by a factor of 12. Since triangulation process also divides the cells, the total effect of triangulation in the core region is to increase the number of cells by a factor of 24. As a result the number of incore cells becomes more than 4000. Since CPU time and RAM requirements increase with increasing number of cells, this kind of triangulation was estimated to be too expensive (if not impossible) to run, because of the RAM limitation of the available computers. Accordingly the triangulation process was applied only to the cells outside the core hexagon. Before the triangulation of the out of core cells, the graphite definition is changed from cylinder to hexagonal prism as in QUARTZ model. The triangulation of the out of core cells is a very long, and tedious job which required more than 60 hours of work. In this process triangle surfaces defined according to the QUARTZ model and all the out of core cells are redefined by using these definitions, and previous surface definitions of Simplified model. At every stage of the development geometry integrity checks were done to insure the accuracy and consistency of the model as compared to the Simplified Model. The result is called the Triangulated Model; it is a combination of the Simplified model and the QUARTZ model. Figure 2.10 and Figure 211 show two different views of the triangulated model. This triangulation was done only for the initial 12 axial segments; four additional axial segments were added to the bottom later on for obtaining the constant albedo at the bottom. Two test were applied to the triangulated model, a geometry test with 100 million histories showed that there is no gap between cell definitions and that all of the cell definitions are correct. In addition, criticality calculation was made and the k-eff obtained was 099719 very close to 1.00. These tests support the integrity and accuracy of the model. 32 AAA Z/T T11\7)6II\VVV\1VVV V\/\\Vv\ /VL/\ I VV\/\/\ \/V\AVV /VZ VVLzl A 'V\/VVV /\ &LL V\\AVVVVV\/\/VV/A/V A \ \- \ A A \ Vv_/ VVVVV A/VVV\AAA VVVV Figure 2.10 Triangulated Model (x-y view) 33 \ Figure2.11 Triangulated Model (y-z view) 34 2.3.4 13 Symmetry Incore Fully Triangulated Model As mentioned in the previous section, to triangulate incore cells is not an attractive option. As will be discussed in Section 33, for incore cross section homogenization, the volume fractions of MCNP model cells falling into each triangle are required and there is only one tractable way to obtain these volumes which is to use the MCNP volume calculation capability and the stochastic volume calculation option after triangulation of the cells. As seen from Figure 212 there is amost a 13 symmetry for incore triangles By using this symmetry all the volume fractions can be obtained by triangulating 13 of the core. Figure 213 shows the 13 symmetry triangulated model. In this model every small subregion (portions of fuel plates, water channels etc.) of a triangle is an individual ell. The model was geometry tested for 100000 and 100 million histories and passed both tests. As will be discussed in Chapter 5, this model is a very pron-dsingframework for the future research. 35 ir-- D- L i I 71 - I r, I I i - 2 Figure 213 I I . I I I 0 . I . I : . 0 2 The 13 symmetry boundaries (note that this is not an exact symmetry because A-ring has only one fuel element and 2 dummy elements) 36 Figure 2.14 The 1/3 symmetry trianguhdal core model (x-y view) 37 CHAPTER 3 PRE-PROCESSING9 PROCESSING AND POST-PROCESSING 3.1. MCNP INPUT PREPARATION AND PRE-PROCESSING PROGRAMS MCNP input preparation involves two parts: the model dermition and the preparation of tally cards. After the Triangulated Model is generated, it is used in separate ways for cross section generation and tallying of the surface flux and currents. his section discusses the tallying process related to homogenized cross section generation part. 3.1.1. Tally Cards To tally the required data for homogenization, only the 4 type tally cards of MCNP are used. Without any multipliers, the 4 cards provide the track length estimate of MCNP cell fluxes. For reaction rate tallies the atom density data obtained from the Triangulated Model criticality test run output is also required. By using these atom densities and multipliers for absorption, total, elastic scattering, and fission cross sections, and for vEf, reaction rate tally cards are prepared. To tally for axial nodes over portions of the MCNP cells, tally segmentation cards are used. 3.1.2. Stochastic Volume Calculation using MCNP MCNP calculates cell volumes and surface areas as one of the fu-st stages of the run, but it cannot calculate the volumes and areas of asymmetric, nonpolybedron, or infinite cells. Since most of the cells in Triangulated Model are asymmetric, the volumes of this cells are required for 4 tallies. These volumes are found by hand calculations if the geometry is simple, but if not, the stochastic volume estimation of MCNP is used. The stochastic estimation is simply a ray tracing process. 'Me procedure is described in detail in the MCNP manual [B-11. Since the process is stochastic, the limiting factor on the accuracy of the results of this calculation is the number of histories followed. For the stochastic volume calculations in 38 this thesis 100 million histories were used and less than 2 statistical eror was obtained for most of the cell volumes. Since only part of the volumes are obtained this way, this statistical eror is not included in the final error calculations described in Section 33.2. 3.1.3. Segmentation As mentioned before, the Triangulated Model is segmented in 12 axial layers, but subsequently anged and 4 more layers added to the bottom of the lower tangle layer. These segmentations and the segmentations for incore tallies are done by using the FS4 taHy segmentation cards. The required segment volumes for asymmetric cells are obtained by partitioning the volumes found using the methods discussed in the previous section. 3.2. MCNP RUNS FOR OBTAINING CELL FLUXES AND REACTION RATES The input files for MCNP runs are ready after the model implementation and preparation of the tally cards. Because of memory lmitations, these input files must be used for separate MCNP runs, of which 6 runs are for tallying all the ells in the core hexagon, one for the out of core portion of the original Triangulated Model and one for the four additional layers starting from the bottom of the fuel cells. All MCNP cases were run on the SIN Sparcstation called mitrsun, using the same initial source file (SRCTP) to repeat the same simulation a number of times. Since mitrsun is not a dedicated machine for this research, most of the time, the runs were made sharing the time with other jobs running on the machine. This time and memory sharing limits the size of the MCNP jobs in that, if the required RAM is larger tan the available RAM at that time, the job cannot be submitted. Also if the time sharing is done without any niceing, time is shared among the submitted jobs equally. Tis was the case most of the time. Since during all the runs, there was at least one other job, the CPU times given on Table 31 must be multiplied by 2 or 3 to get the elapsed time for one run. Table 31 shows the resulting CPU times and k-effective values for each MCNP run. As seen, k-effective results for all the incore runs are the same except of Run 1. During this run the process was interrupted as a result of a power surge, and MCNP used a different source file when the process was restarted. 39 Model with 260 cycles of CPU time used 3000 starting particles (minutes) K-effective Incore Run # 1 1978.25 0.99916±0.0011 Incore Run 2 1979.47 0.99714+-0.0011 Incore Run 3 2183.69 0.99714±0.0011 Incore Run 4 2099.01 0.99714+-0.0011 Incore Run # 5 2103.12 0.99714+-0.0011 Incore Run 6 2003.21 0.99714-+0.0011 Out of core runfor 12 layers 3196.00 0.99719+-0.0012 Runfor 4 a"tional layers 2308.26 0.99524±0.0010 Table 31 The comparison of CPU time and k-effective results for 40 MCNP tally runs 3.3. THE HOMOGENIZATION PROGRAMS SCHEME AND POST-PROCESSING The node-homogenized cross sections are obtained by flux weighted volume averaging using the computer programs written to process the MCNP tally output files (MCTAL files). For this job, 13 programs to process incore data, and 2 programs to process 12 and 4 segment out of core data were developed. Some of these programs are given in Appendix B. 3.3.1. Homogenization Scheme The flux weighted volume averaging formula for homogenization can be given as the following: g R,9' VOID IJ ( VD 09", where, 9 homogenized cross section for energy group g and triangular-z node j, Rg = MCNP reaction rate per unit volume for cell i, 01i) = volume of the portion of cel i that is in triangular-z node j O(Y) = MCNP flux density for energy group g and for the portion of cell i in node j. 9 To find the volumes for incore homogenization, the 13 symmetry model of the core was run using the stochastic volume estimation and the resulting values were used as the volumes in the equation above. For the out of core cases, volume values are the segment volumes of the cells given as a part of the input. The homogenized cross sections computed are the total cross sections(l, absorption cross sections(l), fission cross sections(l? and fission neutron production cross sections K?. The edited MCNP absorption cross sections do not include either the fission cross sections or the (n,2n) cross sections. The group-togroup scattering cross sections cannot be tallied. They must be obtained from neutron balance. Details of that procedure can be found in the thesis of Kuo [K- I]. 41 3.31. Calculation of the Statistical Errors Since every MCNP result is accompanied with a statistical effor, the calculated cross sections also have statistical erors. Since each MCNP result is a mean value, to calculate the standard deviation associated with the cross sections the following NW formulae [K-21can be used: If u=x+y or u=x-y then a2 u =02 x +2 If u=x*y or u=x/y then (au/u)2=(Ox/x)2+(Cy Y Y/ 2 where x and y are the means of two different quantities having statistical uncertainties and the a s are the standard deviations. If u = c * x where c is a constant, au can be obtained by multiplying ox with the constant c. 42 CHAP'TER 4 RESULTS The results presented in this chapter are divided into two parts: incore results, and out of core results. To indicate how nodes are identified a 2-D map of the quartz model is shown in Figure 4. I. Indices I and J specify the location of the triangular nodes. The index K specifies the z4ocation of the nodes (K goes from bottom to top). To be consistent with the results obtained before addition of 4 layers (Appendix Q, the nodes above surface 85 are numbered 112 srting from that surface and going up. Below surface 85, K is negative and decreases from the surface downward (as 1,-2,-3,-4). The flux results are normalized to one starting particle (fission source) and to obtain the fluxes in units of neutrons/cm2/sec the MCNP flux results should be multiplied by the number of fission neutrons per second corresponding to the power level of the reactor. That factor is given by: PN = P I Q v I ken) where, P Reactor power level Watts Q Energy generated per fission ( J / fission v Average number of neuuxm generated per fission kef = eutron Multiplication Factor. If both the numerator and denominator of homogenization formula are multiplied with the same constant, the result does not change. Therefore the flux results presented in this chapter are not normalized to power. 43 4.1. INCORE RESULTS The incore homogenized cross section results along with the calculated statistical erors for the 12 layers of 24 triangles are obtained by using the scheme discussed previously. The complete set of results are presented in Appendix C under the fe name xchonOn where group is the fast and group 2 is the thermal group, and group boundaries are 0.625eV to MeV and to 0.625eV, respectively, also errors are given as the ratio of error to mean value (the result). These results were obtained by using the specially written programs named as xg*.f and xg**.f. The accuracy of the results and the reliability of the software were tested by regenerating the same results with an entirely different logic which is reliable because of its simplicity. The software written for comparison, sibelf and the results labeled rslts are given in Appendix B. The results given in rsIts and those of Appendix C match to at least significant digits after the floating point. This test process is a strong evidence that the processing of the MCNP results i correct. 4.2. OUT OF THE CORE RESULTS The out of the core results are discussed in two parts: the initial 12 segment Triangulated model results for regions above the bottom level of the fuel and the 4 segment part below the bottom level of fuel (which from this point on wl be referred to surface 85 or simply 85 the reference being to its MCNP surface number). 4.2.1. ResWts for the Nodes Above the Bottom Level of The Fuel (above 85) This part of the results was obtained by running the program prohxlnf of which listing is given in Appendix B. The complete list of cross section results is extremely long and therefore is not given in this thesis. However the results have been saved in a file named hxIn.ou and packed with all the files in the same directory for possible future use. Some sample results are given in Table 41. These results display radial change of the cross sections and flux starting from the graphite reflector, crossing the D20 reflector and core radially, and ending at the other comer of the graphite reflector hexagon at axial node K6. Statistical erors are given as fractions of the results. 44 1.11 J.) 17 J7 Aai \\Y 11 // V \,V/I\ /'VI\'/V \'AN//Vv\'/\ \J \,\J// 1/\A1\1f \.//' ,/\V\/V '\4 v ZZ 'VV LZ \ -- /,\ A AA \ \ V \ \J/V V V V \Ak/ V V \\ \/\,//'V\/'\\/VV \/ VVVVVV\ \ RaALaL MakA Figure 41 2-D nodal map of QUART7, model showing the I and J indices user in the representation of the results, also K is the index for the z-direction 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . en 0% 00 D W) 'IO kn kn 4 0 en O rle -Ici -- I'D (4) o 0 "It eOlO SD 100 0 0 0 0 00 en ci ll v m Coco 010 OCCOCCOO00000 000 0 0 10 0 0 10 0 0 01010 CIO l M-Z Oc 0000 C C OCCOCCOCC 0 0 en . . . . . . . . . . . . . . . .. q 101010 V le m 0 . T T T TT T T T T T T T T T T PoNowino"Co 0 8881:8888 0 0 qP 0 0 0 0 0. 0 OIC616 0 ,-t in Oe "r-m r- w %n0 O I-e ,::,C 00 o 00 18 a, a 0 0 0 0 0 0 Vq$ 0 0 C 0VIVP 0000 O in 110, 0 %n " 110, a, .m en,t a," m -CC- - kn - ON -- - ON - -l - e-n 'IT ci t 0IIT r-V1'IOr"Itle V 0 * r. w v - W S. eOa k l tn kn le l m kn tn in kn v m m eq le C4 V m m 1^ in 1^ 4n V, m %n %Cle le 0 V >1 1.1 9, a, a,z F- eq 0 c 4 m pa w w w i c in 0%,-e m VI) CIA 4 M C4 C4 C4 ei m c m o w v ei or; ft M CZ .4 c "t cc 0 w*,, v kh m m t w M e C4 c in IC mt v V 0 r v w M W C4 c c -.6 c ei 9 in 0 w C4 4n ei 4 c 06 c It x O"r-"W)r-cn-cnn" 10 c cli In ! R R R R ! R W) C4 r m 0 0 en en rt ' V V O w %A O m C o w m 4 C4 Is en IDc4 r. r- en 0 Nor w t m C C4 c2NV 1"' '01 I 't MO ID %n C41 1" I 00 O ----- . . i . . . .. 0 0 C4 U -14 m rR "It r- CR ll I C4 I VI ' I ------------------------- I I 0 C r a, kn QN r m m R R 1^ M 0 %OID t10 ID r lld: ci R C4 a, - r- in 1 9 % w Z w %Cr- in f r q " r C4 Q M eq C ' eq w IR 1 I I m M " C . . a m N cpkm 'IOm s tn w % C IZ rc R R %n un C4 10 C4 . "C V VI I I 9 Ali C4 kn a, O m m eq %0 %n0 a *, r- V r 9 q - - %nIn I l* 4 C ( %C C ID - I "i 1 five M VJ'M`tM' 99 9 1,01", 9 it I 9 9 PI Cod in V %nV %nle le %nle o le 11 1^ V a, C4 0 M C- V %na, t- C4 in C4 r- w %nr- 0 - C4 4n ci cn li ll lll R R o in Z kn 4n m PPI 1w mimic"l,- 10 %C C4 %C C4 4 ID NI %C 00 C4 46 ) a 9 eq 4 9 V ID ID C4 t m - r- 1*1C4 o NOrIn kn v^ w m %nz w W e - %nm r m C4 v 'I'le en or- a-, - r- ok "C cn M V %n M ; 6 c 06 06 C4 - w C qle4r,; v V 0 w rr- W V w M 4 v - r 0 " 0 r co rI I v in m w %C%CM V w " r 0%- eq 8 8 m t- C4 C4 M m in C R R R R R C! IR Cocole 10 %n%Cv 4n C4 8 00 V M le le t- I r- v r ell %n M %OW w o 0 4 0 V V - rI'D m %nID r- tn w m w W kn a r%n w "t , %C 0, m O ci r 01 "It v W w w w w %n%Oe4 w V P 0 r r- 00 e4 00 (7% W = 4 2 w " m ell'Ain %C r c7sC 0 o 14 m 00 U M r m %n IR .1 "It -----------C---------------co 4 0008 ---. . .. . . . . . . . . . . . 0 x 0 R R R R R C4 No WI - I 99 0 m V 4 w V 0 000 0% 1 I m e4 r- C1 %O %C Un 10 cn IC 'a 4 cc WIcc WI , v R kn M C4 t M C4 %nW V - %CM C4 0% tin %Ce4 1#1kn W) W) - cn ! In r cn C D O In C4 w -1",Iw C ""'I" " 19 'ro .4 " C4 IC 10 r- 00 01 cn en eq %O It 4 'A LI .2 Iu 9 Ili 'IT 12 4.2.2. Results for the Nodes Below the Bottom Level of The Fuel (below 85) The homogenized cross section results for the nodes below surface 85 (which is the bottom surface of the fuel) are also extremely long. Some sample results are included in Tables 42 and 43 which show the axial distribution of flux and cross sections for two tangular nodes: Triangle 1,J = (1 1, 1).and Triangle 2 IJ) = 17,7). (See Figure 41) 4.3. SURFACE FLUX AND SURFACE CURRENT RESULTS 'Me results for surface fluxes and surface currents were obtained by Kuo and the description of the procedure used to obtain these results can be found in his thesis. 'Me results are voluminous and are presented neither here nor in his thesis. The general srategy used to obtain the results was to trick MCNP by filling exactly defined triangle surfaces with the universe of the entire model for incore cells and by tallying the surface fluxes and currents directly for these triangulated portions of the model. 4.4. GROUP TO GROUP SCATTERING Since MCNP can not provide group-to-group scattering cross sections, they need to be determined from neutron balance. his portion of the data gathering process for QUART7 was done by Kuo and is presented in his thesis [K-1]. Also CNEFDdiscontinuity factors were found by Kuo. Some difficulties encountered with the group-to-group cross section and discontinuity factor calculations, which for some cases come out negative. The problems and possible causes of these negative results are, as in his thesis • Negative fast to thermal group scattering cross sections were found. This phenomenon may be caused by statistical fluctuation in the net currents or the absorption cross sections, or from the failure to include up-scattering and n-2n cross sections in two-group neutron balance equations. • Negative CMFD discontinuity factors were found. The negative discontinuity factors can result in loss of the diagonal dominance of the matrices used in QUART7, which can cause the solution to diverge. One way was found to avoid the negative discontinuity factors, namely to increase arbitarily the diffusion coefficients so that the factors which cause a match with the reference leakages will be positive. Some additional discussion of these problems is given in the next section and in Chapter . 47 h C,4 ON(14 C14NO C14 cq 0 m q (1 m m tl- tn tn W W W)VI in tn W) tn W m m m m q 9.9.q u-99991.9qq9.919q. 10 14 C X "-4 Q-4 cn cN Cq cn cn 0 cn m C I- t- oo n 0 r- w W 00 rw N cn 0" 'O C4 00 eq r w W tn eq %n eq kn eq it-, N cli N W) Cq chose 10 r- wl 00 M2000 coo co en " CN o C4 cn eq m N wl en 'CO W f3 cn %n r- 11 I-i rl--4 11 cn 00 Cq 00 x en 00 ;t r- r- N r- 00 00 00 Itn r- rcn r- (n P n r- n r- VI) n r- en n r- ,: IV elillcli I efi li 41(li 4 W) ON 01, en 41cli r--: li t vi r- r- OA fi r-: cli r-: i I I W t009qoOO99 80414ftm -4 -4 I" l." 00 rtn 0 I 00 ON 00 -4 l." -4 I-- 4 Cq --116 9q2ggc ooco 99 w WW6 -- I 1-4 1-4 I-- 010, C ICT6 I-- -- q 1-0 1-0 W) 't 0 W) m 00 tW-1 C, ON 00 --4 l, 00 r- C- II-" 1-4 1-4 -* § VI) 00 106 W) eq fl- "C 00 C- as 00 Cs N N VI) W 00 00 W) N C4- q N NMNMNSM Lu r_ r 114,E 8 en C." Ao -1 A tn = 00 N . q oq C4 . cip N r- C 4 so P4 o C4 I 41 %n4 'IO -z N eq 1eq cn v VA [o 00 co c7A WI -4, O Iq Iq oq m 0 N NOC IV N - eq -4 4 " N r- loo CN in -4 4 4 -4 4 i I t8 t- cn It. I09 we in ON -,41-1 1-4 W) v tn 4 06 4 1"Olool"'lloo W) C4 r- -4 00 C14 00 CNm C o OT6 a, d a, r- C ON rl- 00 r- W) C- in 1-4 " (4 4 1 4 lu 4 la C14W) w ) o 0%OAN w M C-4 C,4 . . . . .. Rt M C14 Cf) CIP) ten W f) Mt ss N ON 00 It,- tn .- CN 1-t -4 cq tn cn .!;: CA in t00 tCf) 4 ir- 06 4 00. N. CA N. 4 C-i ;x - s C'i eq et) oc 1-0 Cf) n r- 00 " C4 C-i";Icql W) INA C'i C N4 C'i Mt tn 00 oq oq W N C; in 00 -.4 1%, "I0 s 4: en 11 1-i -4 11 0-4 r I en m en I Ca cn r m 00 N r- C4 r- %n 00 r- r m en Cq 00 008 N en 1 1 00 1 18. 0 rl." o %nN 9; a, N tn As's la0 t 0 cn n N--* en 0 t- - w 00 - f- o ID cn 00 cn r ON00 In PM r- 00 r-I 0 r-I i R r- - r-loo r- 0 r- 0 r w cn 8 r- CN C4 cn o In 9 00 r- n w Ix 0 cn c 00 00 Cw A cc 4 N N C,4- N c (n en C4 N 14 en 46 e4 ;6 i N N N a ,w ON CIF) 4 C-4 14 lu l." 1-4 1 O -I MI0 1 49 4.5. NEUTRON BALANCE The programs to calculate the two group neutron balance were written by Kuo, originally to obtain group to group scattering cross sections. Because of the inconsistency of the results, another program was written to obtain one group cross sections, fluxes, surface fluxes and surface currents from the two-group results and to check neutron balance for one energy-group. The procedure and program were also tested by the author. For both incore and out of the core results this balance check is failed (Some of the results of this balance check are given in Appendix D). It is important to recognize that, for incore results, neutron balance should not be expected.7he surfacefluxesand surface currentswereobtainedfor the surfacesof triangles, but the cross sectionsand nodeflux were obtainedfrom a homogenizationschemewhich uses MCNPflux resultsfor group of cells not bounded by the triangle surfaces. The lack of balance suggests that either there are invalid approximations involved in the process or that some of the data obtained is either incorrect or includes too much statistical error. These possibilities must be investigated for incore and out of the core separately, because the procedures for these two cases have some major differences. Incore results The accuracy of the homogenized cross sections was established by regenerating the same results semimanually for an arbitrary triangle using an entirely different programming logic. The results had very low statistical effors. These findings suggest that the eor comes from these results it is related to the assumption that the flux distribution is very similar for the neighboring rhomboid core assemblies and does not change much throughout the assembly. According to Kuo, the processing of his results are also correct, therefore; again only the MCNP results can be questioned. In his tallying process, Kuo had to make several rims for different surfaces of different cells because the universe-fill scheme does not allow him to obtain all the results together from the same run. This might have caused some inconsistency in the neutron balance, because the model is changed slightly for every run. To expect a neutron balance in the end, all of the separate MCNP runs should be the repetitionsof the same simulation,otherwisethe resultscome out irrelevant. Out tcore results Again the models used for the homogenized cross section part and the surface part have some differences. Kuo explicitly divided the cells into segments to obtain node top and bottom surface results while the author used the Triangulated model directly. These differences might have affected the simulation results. 50 For the ells and surfaces in the graphite nodes, the statistical errors are very high; even zero flux results are obtained for some of the triangles because of lack of sampling. Therefore; it is hard to expect any balance in this region of the core. 4.6. GENERAL TRENDS OF THE CROSS SECTION RESULTS This section aims to present some portion of the data in a meaningful format and investigate possible causes of filure of the general procedure. The distributions presented in Table 41, Table 42 and Table 43 are represented graphically in Figures from 42 through47. Figure41 shows the locationof the traverses in the radial direction. By looking at the results presented in Appendix C, Table 41, Table 42, Table 43, and the figures, some general observations about the triangular node fluxes and homogenized cross sections can be made. They are itemized as the following: Incore homogenized cross section results (Appendix Q have very small errors. Average and maximum statistical errors are (the first number is for fast and the second is for thermal group): Flux Total Xsection Average error 0.5% - 09% 0.6% -1.8% 2.0% Maximum error 0.9% 1.3% - 28% 3.1% - 26% Ile eors 1.7% Absorb. Xsection 1.7% Fission Xsection 1.8% - 29% 4.2 - .1% for the flux results are very small; because of the high value of fast flux in the core, the percent error for the fast flux is smaller. Statistical errors are higher for the cross sections -especially for fission- due to the fact that sampling is lower for these quantities. Te absorption cross section percent erors are lower for the thermal group, because the thermal absorption cross section is higher then the fast absorption cross section. These are the expected results for a very compact core with the boundary between the energy groups set to 0.625eV. Another observation is that most of the total cross section consists of the scattering cross section. 5-1 N 3) - - -------- -- m ---------- rl(D Ln 10, ol------ ---------- 0C (1) S C\j W" II 2 - .c -0 W) - C:) ----------- X U) 'a 10 a - Wm a 1; 0 -- ---------- W ------------ cm v 0(b 9in IT (h ,W (b C IT 9M 0 0 0(b 9cm v 0(b 9 uo.qnau aajnos jad xnjj Figure 42 Radial flux distributions (axial node K=6). 52 O 000 6 n W 10 O c I-j N 0) rn t CC) cj fl- CA V) A CD C.d U') 0I- 1-1 .a,. N C C.. L. j CI) a 04 P" 11 :111 - V) W A . I= 10 .- la la 0 W N . Qj a 0 E 0 - W W IC 0 r. U') 4"d 0 r. 0 4" Z CM IC 4" W) 0 10 C Ln - 0 1-: LO 6 0 6 1; I= M (w:)/I) suoilaas sswa pazwagotuoq apoN 9 Figure 43 The radial distribution of homogenized cross sections (axial node K=6). 53 09 -1 Ij m 00 CD A 0I- LO 1-1 1. C.10 'IT -3 j CO 0 .4" I" CV .11% I - VI - Q W2 w la 0 C la la aj 64 100 U" 0 fl- C 0 .0 Le) la (A 10 CI) la 0 0 0 (D 1"Up & UI) UU U SOJJ3 W a OAT;RJOH Figure 4.4 The radial distribution of statistical errors (axial node K=6). 54 de w ------------ 0 rr- 1-1 11 1-1 17 m 11 .d w Iz ------------------- r. N m Q .10 0 -------------- . L. 12 co 'R W) W X c 46.d 0 c 0 16.6 CI) r. .0 , I CA la CM 7; X Iw (h 0(b 904 0 9 (umiInau aamos 0 (D 8 ci ad) xnl,4 Figure 45 The axial distribution of fluxes for the 2 energy groups in node (17,7). 55 C\j ----------- ---------0 rrZ M 11 - -- --- --------- -- -------- C-4 co ;d N - .,=w Z Z fl- r a = - C Ir- 4j .% 11 -9 A w 10 0 ----- ------ - S. CD 'a (A = C 0 .0 . U') *W rj %- w 0 M r V) CA C 0 "W = Q :2 CI) Cj .!: ,FL .n0 Cj ----------- --- ---- ----- -0 'n 04 0L. - .1:4 Ci X (M -,etE co 6 aIP C 0 0 0 6 (wa/1) S01133S SSOj;) anuagOWOH Figure 46 The axial distribution of homogenized cross section results for the 2 energy groups in node (17,7). 56 r- r: 11 0 I--, -It a) C 6. co 11 A z 6. S- r- A W 0 4i C to . Li '7 (A Q (m Qj L. CI) 4.0 0 C O .C 4" n Ii 0, CIj Ci SJOJ13 6 0 Ci 11831jSIjRjS aAI.7131all X Figure 4.7 The axial distribution of statistical error for the 2 energy groups in node (17,7). 57 Table 41 shows that the cross sections for graphite -especially the fast group and those for outer triangles- are accompanied with unacceptably large eors. Values of 141 eor mean hat there are only one or two interactions occurring for the approximately 250*3000 srting particles. Since the flux is low at those areas, they can be used (cautiously) in subsequent calculations. However they can not satisfy the nodal balance. Erfors in D20 region are much lower because of the higher fluxes (especially thermal). The triangle samples from J=8 and J= 13 correspond to the Control Blade Ring where the control blades and water holes are present in the Al blocks. Te errors for this ring are as low as the ones for the incore portion. The gradual increase in the ratio of thermal flux to fast flux with the radius can be seen nicely from Figure 44. Table 42 and Table 43 shows the axial distributions for two triangles: the one given as Triangle I (node i=1 1, j= 1 of Table 42) is in the outer graphite ring but is on the side of the hexagon so that it sees the core much bet ter than the corner triangles. Hence it has much better statistics than the comer ones. However, the fast energy group results are still unacceptable with their more than 50 eor 'Me thermal energy group results have acceptable errors. 'Me non-zero thermal flux values suggest that there is some leakage from the sides of the graphite which might bring the arbitary assignment of a hexagonal boundary into question. However the k-effective is not affected, indicating that the coupling of the neutrons in the outer parts of the graphite to the core is negligible. Ile flux distribution is given in Figure 45. It is higher at the bottom and lower at the top nodes, probably because of the higher absorption cross section of the H20 at the top next to the core hexagon (wider portion of the core tank) comparing to that of D20 in the reflector tank surrounding the bottom portion of the core tank. The other triangle node i=17, j=7 of Table 43) goes through heavy water at the bottom nodes and light water at the top four nodes. Figures 45 and 46 show axial distribution of fluxes and cross sections. Ile thermal flux shows a distribution similar to that of Triangle I but drops more significantly because of the light water existing at the top portion. 'Me fast flux is also higher at the bottom. Fast absorption cross sections are much higher in the top 4 nodes 2 to 4 times), although the total cross section is only slightly higher at the top (D20 balances the effect of H20 microscopic absorption cross section with its scattering cross section). The thermal total cross section is higher at the top because of two orders of magnitude higher thermal absorption cross section. One thing to remember about the cross section behavior is that the fast group starts at 0.625eV a rather low cut point. The distributions of eror for both triangular nodes increase as the flux decreases. Errors in both energy groups for Triangle 2 are acceptable, also the eors in Triangle for thermal energy group are acceptable (around 10%). However, again, this kind of eror affects neutron balance significantly if all the data is not obtained from the same simulation run. 58 These observations show that the cross section distributions are consistent and match with the expectations. Ibis is an eidence about their accuracy. As mentioned, there is a suspicion about the initial assumption that flux shapes among portions of a rhombus shows similar behavior. To test that flux distributions in two different fuel plates of a rhombus and in one of the dummy elements compared with each other. For this comparison, fuel element B-7 and the neighboring dummy element A-3 were selected (both contributes to triangle (IJ)=(4,2) denoted in core coordinates). Figures 48 through 413 show MCNP axial flux distributions for Aluminum of A-3 and two fuel plates of B-7 of which Plate is the closest plate to A-3 and it is completely in the selected triangle, Plate 15 is the farthest fuel plate to A-3 and it is completely out of the triangle. In these figures, according to MCNP convention the segment nmbers increase from top to bottom. These flgures show that the axial flux distribution differs significantly among the portions of same element, and among the neighboring elements. After these observations, one other investigation for incore results can be made: Is the assumption that flux distribution is the same throughout a rhomboid shaped element, and the flux distribution does not change significantly between two neighbor incore elements? For these investigations by considering that if there is a significant difference exists, it is between fuel and dummy elements. 59 FL',JX li N DUMMY 1 n0 0 [,I U ry Idi < O 0 I __j I Ln I 0 0 2 4 6 8 SEGMENT BIN 10 2 4 6 NUMBER Figure 4.8 MCNP axial thermal flux distribution for Aluminum of A-3 (segments are numbered from top to bottom). 60 11 0 A N U MM Y A- 3 . . . . . I . . . . I i -j U rf, aI __j I ,II - - - - CD 0 2 - - - - - - - - - I 4 4 6 a SEGMENT-BIN 10 2 . I . NUMBER Figure 49 MCNP axial fast flux distribution for Aluminum of A-3 (segments are numbered from top to bottom) 61 6 FLUX IN FUE:- 3-7 ,I- 0 L.L-j -.- I U r, a_ .1 I I Ln 0 0 2 4 6 8 SEGMENT BIN 10 2 NUMBER Figure 4 10 MCNP axial themml flux distribution for Plate I of B-7 (the closest fuel plate to A-3) 62 4 FL!,!X IN FE1C) 0 I. CD . . . . . . . . I . . . . I . . B-7 I I I . . . . . I i iI I I L.Ij U Of aI I 14I . . . . . II I I I I . . . . . . . . . . . . Ili 0 2 4 8 6 SEGMENT BIN 10 2 NUMBER Figure 4.11 MCNP axial fast flux distribution for Plate I of B-7 (the closest fuel plate to A-3) 63 4 F L UX N 5_ FUE- 7 0 L.J I U ry a. -j -j Ul I (-j I . I II .1 . . .. .. .1 . . .I . .I . . 0 2 4 .I .I .I .I . . . . . . . I . . I . SEGMENT I . a 6 BIN I 10 I 2 NUMBER Figure 4.12 MCNP axial thermal flux distribution for Plate 15 of B-7 (the farthest fuel plan to A-3) 64 4 FLUX CD 0 -1 O I FUEL B-7 IN . . . . . . . . . . . . . . . . . . . . . . . j L.I.J - i L) Of CL 11-1 I --I I 41 1 C) . 0 2 4 . I I I I- I I 6 I I I - 1 10 8 SEGMENT BIN I 2 NUMBER Figwr 413 MCNP axial fast flux distribution for Plate 15 of B-7 (the farthest fuel plate to A-3) 65 4 These observations about axial flux shapes suggests tat the assumption was not a gotodow, but it is the only path the an be followed without tangulating the, entire re. On the other hnd, without a triangulation, the homogenization process sould work for a rhombus providing that the surface currents out of the rhombus can be obtained from the same run. For testing the homogenization scheme, a model consisted of only one fuel element (wiih smaller length to save from runtime) was created. With only one nm surface currents, reaction rates and fluxes were tallied. for one energy group and these results were processed to-obtain cross sections and leakage out of the rhombus. The MCNP results and the proce program is given in Appendix E. The resultsof the processing program are.Average rhombus flux : 1.34163E-02 Absorption cross section : 3.46784E-03 Total cross section : 3.75824E-01 v sigma fission : 6.14328E-03 Fission cross section : 2.46291E-03 Neutron balance results are: Total eakage :2.45090E-03 Total loss :2.49743E-03 Total source : 2.50364E-03 Therefore, the residual from these was found as: Residual :6.21402E-06 The ratio of the residual to total loss and total source are very low: Residual Tota km : 2.49817E-03 Residual / Total source : 2.48199E-03 These results are the indication of neutron balance. This shows that the procedure can satisfy neutron balance, if the complete triangulation can be achieved and surface currents can be allied with the reaction rates in the same run. 66 CHAPr-R 5 CONCLUSION 5.1. GENERAL EVALUATION OF THE RESULTS In previous chapters, the homogenized cross sections, calculated for each node of triangular-z mesh QUARIZ model of MIT-H, were presented. Comments about the results and thek accuracy, and about the neutron balance results were made. The lack of neutro blance was discussed and some of the mystery surrounding it was removed. U present chapter . i tese discussions. Evidencesupportbigthe'accuracyof the cross section and node averagedflux results (at least within the limits of the procedure) can be • . I as: Past experience with the original model and tests at every step of the model development sow that, the MCIVPmodel Triangulated Model) represents MrM-II correctly Section 23). • • The reliabilityof the processingsoftwareis demonstrated(Section4 ). begeneralbehavkwotbotbfluxandcrosssection&stributionsmatchesexpectations(Sectwn4.6). Despite this evidence, nodal neutron balance could not be otained. Since homogenized cross sections and fluxes were obtained fim te same group of runs and same proven processing programs, the mismatch must be betwom them and the sur6ce-currenttsurface-flux results. 11hereare several points in the pocedure that are believed to be the reason for the mismatch: • he model usedfor sur.faceflux and currents differs in some aspectsfirom the model used for cross sections. herefore the simulation cannot be repeated exactly (Section 45). • For the incoreportion, unlessflux shapesthroughouta given rhombuswereflat, exact nodal balance cannot be expected. 67 • Sow Ponions of the out of core resultshaveunacceptablyhigh statisticalerrors thittcm only be fixed by increasing the MCNP simulation run tme by at least a factor of 100 (Section 46). • Some oher portions of the out of core results have moderate eors (5%-10%), but the total effect of these erors and the ones fim surface flux/current causes unbalanced results (Section 46). Unfortunately the total effect of al tese contributors cannot be estimated. Some other points about the unbalance can be made: • To repeat a simulation (MCNP run) exactly, the model, the number of histories waked and the initial source points should be the same. Evidence that some repeated runs were not exact is that the keffective of the run differed slightly between Wcore and the out of core runs and also between tose and the surface current and surface flux runs. This shows that the use of the same basic model and the same initial source points does not guarantee exact repetition. On the other hand, five icore runs resulted with the same k-effective. Thus simulation can be repeated only by satisfying all of the given conditions. The sampling size 250*3000 750000) of starting particles may not have been Lge enough to compensate for tins lack of exact repetition, and balance may have been affected. • Even if the lack of repetition is only a few percent for each cycle, after a smal nmber of cycles, the simulation become totally different leading to an avalanche effect, since succeeding source points are the outcome of previous cycles. To get rid of the lack of repetition was not possible with the process used in this thesis. Te tallying jobs were done by following the only path found after a careful search and investigation of possible alternatives. Generally, the paths chosen represent the only practical solution as far as the author and Kuo consider within the capabilities of MCNP. To repeat a simulation exactly requires that tallying should be made without modifying any of the cells. However it was necessary to repeat the calculation several times at least by changing the universe numbers. The obvious way to avoid this is to do the simulation only once and to tally everything from this one simulation. Unfortunately tis procedure is beyond the capabilities of MCNP at present. In the following section, computer facility requirements are estimated both to get rid of unacceptable statistical erors, and to complete this kind of MCNP run in a easonable time. 68 5.2. COMPUTER FACILITY REQUIREMENTS The comments about the facility requirements given in this section takes the SUN Sparcstation mitrsun as reference. Therefore requirements can be translated as the nmber of times current capacity. Table 5.1 shows a summary of the data relevant to the computing resources used during and after each MCNP run. This data is used for making the estimates given in the following subsections. The runs with name Run#* and Vol Run are for incore cells; mit8c is for the 13 symmetry model; outhexy, outhxt2 and outhlOt are for the out of core cells. MCNP RUN #of cells & run date CpU time k-,ffective OUTPTfile (minute RUNTPE MCTAL size (MB) -rilesize (B) file size(B) Run #1 913 1978.25 0.99916 2.59 5392939 669872 Run 2 913 1979.47 0.99714 2.58 5392959 669872 Run 3 715) 1210 2183.69 0.99714 5.08 6724855 1586514 Run 4 719) 1210 2099.01 0.99714 5.10 6705367 1565800 Run #5 723) 1210 2103.12 0.99714 5.10 6705367 1565800 Run 6 726) 1012 2003.21 0.99714 3.69 5906727 280.11 n/a Volume run for 10 million articles 1 1051704 Vol Run 82) .913 mit8c run 1173 3.62 n/a 100000 particle run to check geometry outhexv 2706 6004.5 n/a. Volume run for 100 million articles outhxt2 919) 2706 3196.0 0.99719 13.9 10731259 3314861 outh I Ot ( 12) 3341 2308.26 0.99524 6.21 9557675 350221 (8/8) Table 5.1 Summary of the data relevant to the computing resources used during and after each MCNP run. The following subsections ahn to evaluate the computer resources used for this thesis project and to make the required facility estimates for an exactly triangulated model involving 600*16 triangular-z nodes. 5.2.1. Required Memory for MCNP runs Each incore run used 2500,000 words of memory and each one of the out of core runs used 5,000,000 words of memory. The total memory available on mitrsun is approximately 15,000,000 words, but experience indicates that, even if only 10,000,000 words of RAM are used, the system starts to create problems and this affects all functions of the system adversely. For example the system may not allow a 69 user to login. The largest size run with approximately 4000 cells were made by Kuo, and this run tied up the machine for about a week. Since it was a 10,000,000-word-run, the upper limit of the RAM may be taken as that value. The number of cells for the entirely trangulated model may be estimated from the number of cells of 13 triangulated incore model and the number of cells of the out of core models. Thus with 913 large incore cells used in the outhxt2 model and 2706 cells used for the rest of the reactor in the model for the lower four layers, # of incomecells of axial layers)* 3 # of out of core ells for top 12 layers 1/3 model cells) = 12 12 3 42228 (out of core ells of outhxt2 12 * ( outhxt2 cells - 913 # of out of core cells for below 4 layers 1173 4 *(3341 - 2706 12 2706 - 913 21516 2540 Thus the total number of cells required becomes 66248. The definition and run of that large job is impossible for the available machine. Thus another estimate for a model that gathers the required data with only few runs 2 or 3 by using tally segmentation was made. In this case the number of cells adds up to 3519 1793 635 = 5947, making it is a very large job by itself As mentioned a 4000 ell run uses -10 Mwords of RAM. Assuming linear dependence the required RAM for these 2 or 3 runs becomes around 15 Mwords, which exceeds the RAM capacity of mitrsun. The assumption in this second scenario is that tally segmentation can be done without segmenting the actual cells physically. Tis is the case for the cell reaction rate and flux runs, but may not work with surface flux and current runs. Methods for accomplishing such segmentations need to be investigated. 5.2.2. Relation between CPU Time and the Number of Cells In the Model The total CPU time used during the homogenized cross section part alone was approximately 2000 minutes. Since the relation between the number of cells and the CPU time is not linear, being affected by the size of the cells, only a rough estimate for a 260 cycle run with 6000 cells can be made. The result is 8000 minutes based on taking 25 times the CPU time of the outhxt2 run. If statistical errors are to be decreased by a factor of 2 the number of cycles must be increased 4 times. Iberefore, assuming a linear relation, the CPU time becomes 32000 minutes. As mentioned this run must be repeated at least 2 or 3 times to tally everything, since MCNP has a limit on the number of tally cards that can be used. 70 5.23. Relation between CPU Time and the Tallies In the Model Present results and past experience suggest that tallying is not the major factor determining CPU time. Obviously it has some effect, but it is negligible compared to the effect of cell definitions. 5.2.4. Storage Space Requirement During this project MCNP output files (OUTYI), run tracking fes (RUNTPE) and tally files (MCFAL) were saved on hard disks. The total storage space for these files for the given runs in Table 5. is approximately 113 MB. This storage space requirement may be decreased by file compression. However, since RUNTPE files are binary files, the compression ratio is around 66 which is very low, compared to the other text files that have compression ratios around 5. Assuming that the storage space will be the same for a totally triangulated small number of runs, the required space is estimated as 100 MB after compression. If the RUNTPE files were removed, it would drop significantly to 50 MB, but this is not recommended since the RUNTPE files are required for possible restart runs. During the project some space was also used for processing the results. But this was minor compared to the MCNP files. hus; 200 MB of disk space should be enough for both cross section and surface current runs. 5.3. CONTRIBUTIONS The contributions of this thesis project can be summarized as the following: • Although nodal balance for the results could not be obtained (indicating possible erors in nodal fluxes for the triangles) a complete set of homogenized cross section results for the triangular-z nodes were obtained, and in accord with the discussion in Section 46, are believed to be acceptably accurate. • From the MCNP runs of 260 cycles of 3000 neutrons, a tremendous amount of data for the 2 energy groups was obtained. The major portions of that information are: L Flux and reaction rates for every cell (pure material) in the core with 12 equal axial segments. This complete iformation for the MITR-H model of MCNP was obtained for the first time. ii. Flux and cross sections obtained for out of core triangles give valuable information about the distribution of cross sections and fluxes in that portion of the model. The same kind of information was also obtained for surface flux and currents by Kuo) W. Since all RUNTPE files were saved, statistical erors may be decreased by restarting the MCNP jobs using these files. 71 • The computer facility requirements were identified, and some estimates for more accurate analysis were given. • The 13 symmetry fully triangulated model is a very good srting point for future research if the triangulation of incore cells is the intention. One might get a feeling about how the tangulation can be done, by looking at the cell definitions for that model. Also that model with some cell additions can be used for tallying and perhaps the recently introduced symmetry boundary condition for MCNP can be used to obtain results with many fewer number of cells. 5.4. RECOMMENDATIONS FOR THE FUTURE WORK In the future, different approaches should be found to obtain homogenized cross sections, fluxes and surface currents. Some suggestions for these approaches are: • The use of a smaller triangular mesh including only the D20 reflector (the flux in graphite reflector is significantly low). • The triangulation of incore cells with the use of the 13 symmetry triangulated incore model. • The creation of a less detailed model for the MITR-II core, by lumping neighboring cells together through material homogenization. Also options related to MCNP: • Apply the recently introduced symmetry boundary condition, • Make use of the newly added prallel computing capability to reduce run time. In the future, if MCNP has options for tallying group-to-group scattering reaction rates or tallying homogenized cross sections for groups of cells directly, many inherent problems of this project will be solved automatically. Other suggestions would be the use of a CRAY for faster runs or the use of a dedicated and faster computer. To write an in-house code especially for MITR-II may not be an option. Developing a code like MCNP requires thousands of man-hours of programming and years of heavy usage testing. 72 REFERENCES [B-1] Briestneister, J F, Ed., MCNP A General Monte Carlo Codefor Neutron and Photon Transport, Version 3A, LA-7396-M, Los Alamos National Laboratory, 1991. [B-2] Briesmeister, J , MCNP3B and MCNP4 Newsletters, Los Alamos National Laboratory, 1988 and 1991. [D-1] DeLorey,T F, A Transient,QuadraticNodalMethodfor Triangular-ZGeometry,PhD. Thesis, Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1993. [D-2] DeLorey, T F QUARTZ Users Manual, Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1993. [F-1] Fowler, T B, Vondy, D R, and Cunningham G W, Nuclear Reactor Core Analysis Code: CITATION, ORNL-TM-2496, Rev.2, Oak Ridge National Laboratory, 1971. [F-2] Fraser, D A , Statistics: An Introduction, Wiley, New York, 1958. [H-1] Henry, A , Nuclear Reactor Analysis, MIT Press, Cambridge, MA, 1982. [K-1] Kuo, W S Te General Evaluation of the Nodal Synthesis Method in Nuclear Reactor Transient Analysis, PhD.Thesis, Department of Nuclear Engineering, Masachusetts Institute of Technology, Cambridge, MA, 1993. [K-21 Knoll.,G F, Radiation Detection and Measurement, Wiley, New York, 1989. [M-11 MIT Reactor Staff, Facility Description Manualfor the MITR-11,Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1979. [M-21 MIT Reactor Staff, MITR-11brief description brochure. [R-1] Redmond, E L, Monte Carlo Methods, Models and Applicationsfor the Advanced Neutron Source, MS Thesis, Department of Nuclear Engineering, Masachusetts Institute of Technology, Cambridge, MA, 1990. [R-2] Redmond, E L, Monte Carlo Modelling of MITR-11,22.39 term project report, Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1990. [R-31 Redmond, E L, Yanch, J C, Harling, 0 K, Monte Carlo Simulation of the MIT Research Reactor, 1993. [S-1] Selby, L C, Experimental Evaluation of an Instumented Synthesis Methodfor the Real-Time Estimation of Reactivity, NE/MS Thesis, Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1993. [T-11 Tari, 1, 22.39 Term Project and 22.901 Special Problem Report, Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1992. 73 APPENDIX A INPUT TALLY CARDS 74 c c TALLY CARDS c eO 0.625e-6 20.0 fqO c c c e s m f 4:n 4 FLUX TALLIES 4 4902 4912 4 92 0 49322 49422 49502 4 49 4 902 9 49040 49049 49129 4913 4 913 9 4 9209 49210 49219 49326 493 42 4 93 46 4 9426 49432 49436 4 9506 49512 4 9516 4962 6 49627 49646 49647 49726 49727 49736 49737 49806 49807 49816 49817 44405 44408 44409 4 4 410 4 4 42 3 44426 44427 44428 44503 44 505 44 509 44510 44522 44 526 4 4 5 1 8 44 52 44603 44604 44605 44608 446 44613 44614 44617 44701 4 4702 44703 4 4705 447 16 44717 447 8 44719 4 4803 4 4804 44805 4 4808 4481 44813 44814 44817 4 4901 4 4902 44903 4 4 90 44916 44917 44918 44919 45403 4 5404 45405 4 5408 45411 4 54 13 45414 4 5417 4 5501 4 5502 45503 45504 4551.1 4 5512 4 5513 45514 4 52 473 2 4 47 422 47 521. 47 622 4 5522 4 5523 4732 47328 47 428 47429 47 52 4 47 52 47 623 4762 6 47721. 47722 47723 4782 47826 47827 20201. 2 0202 20203 2 02 1 202 12 20213 20223 2 0224 20225 2 04 204 67 2 047 9 7 87 0 2 04 56 204 57 204 68 20469 4 5409 4 5418 4 5410 4 5420 49080 49089 49090 49099 4917 4 917 9 492 0 492 59 493 86 49392 49396 49382 49472 49552 49686 49776 49856 49476 49556 49687 49696 49697 49777 49857 44403 44404 4 4418 44420 44421 44422 44517 44621 44622 44623 44626 44627 44628 44709 447 0 44712 44713 44714 44715 4472 4 4472 44726 44728 44729 44730 4482 44822 44823 44826 44827 44828 44909 44910 44912 44913 44914 44915 4492 4 4492 44926 44928 44929 44930 45422 45508 45518 45528 473S9 45426 45427 45428 45509 4 5510 45519 4552 4 5423 4 552 9 473 64 47 4 0 47 462 47 556 47 561 4 5530 473 65 47 468 47 564 47657 47662 47 663 477 59 47761 47762 47850 20208 20218 20230 2 0462 2047 4 473 68 47 469 47 565 47 666 473 69 47 460 47 566 47667 47763 47769 47865 47866 47867 47 860 202 09 2 02 0 2 0219 20220 20221 2 0222 20451 2 04 52 2 0453 204 54 2 0463 20464 20465 2 0466 20475 2 0476 2 0477 2 0478 2 0480 7 87 1 78752 78753 78754 78755 78756 7 8776 78777 78778 78779 78780 78781 78782 78783 78784 78785 78786 78868 78880 7 8903 78904 7891 78916 7 8936 78937 7 8948 78949 7 97 1 79752 7977 6 79777 7 8867 78878 7 8879 7 8902 7 9 4 7 893 7 947 7 97 0 7 977 7 97 87 44514 4452 44609 4 4610 44618 4462 4 4706 44707 44721 44722 4 4809 44810 44818 4482 44906 4 4907 44921 44922 4 4513 4542 45505 45506 4 5507 4 5515 45516 45517 4552 4 4552 45526 4 5527 47329 473 54 473 5 473 8 47 420 47 452 47 458 47459 47 526 47S51 47 554 47 555 47 627 47 652 47653 47656 4772 9 477 1 477 52 47753 47 82 47 855 47856 47857 20204 2 0205 20206 20207 202 14 202 5 20216 20217 2 0226 20227 2 0228 2022 9 20458 20459 20460 20461 20470 20471 2 0472 20473 7877 78787 78802 78803 78804 78805 7 8814 78815 78816 78817 78833 78841 78842 78843 78844 7 8853 7 8866 49050 49059 49060 49069 49140 49149 49160 49169 49220 4922 9 492 40 49249 493 52 493 56 49362 49366 49442 49446 49462 49466 49522 49526 49542 49546 49656 49657 49666 49667 497 46 49747 497 66 49767 49826 49827 49846 49847 44411 44413 44414 44417 78869 78881 78905 78917 78938 78950 79753 79778 78806 78818 78834 78845 78870 78882 78906 78918 78939 78807 78808 78809 78810 78811 78812 78813 78819 78835 78836 78837 78838 78839 78840 78846 78847 78848 78849 78850 78851 78852 78871 78883 78907 78919 78940 78872 78873 78874 78875 78876 78877 78884 78885 78886 78887 78888 78908 78909 78910 78911 78912 78913 78941 78942 78943 78944 78945 78946 79754 79755 79756 79779 79780 79781 79782 79783 79784 79785 79786 75 fc4 c fl4:n 79802 79803 79804 79805 79806 79807 79814 79815 79816 79817 79818 79819 79833 79834 79835 79841 79842 79843 79844 79845 79846 79853 79866 79867 79868 79869 79870 79871 79878 79879 79880 79881 79882 79883 79902 79903 79904 799Q5 79906 79907 79914 79915 79916 79917 79918 79919 79935 79936 79937 79938 79939 79940 79941 79942 79943 79944 79945 79946 ** cells without segmentation ** 46103 46104 46105 46108 46109 46110 46111 46113 46114 46117 46118 46120 46201 46202 46203 46204 46205 46206 46211 46212 46213 46214 46215 46216 46221 46222 46223 46224 46225 46226 46301 46305 46306 46309 46314 46315 46318 46319 46321 46324 46328 46329 46402 46403 46407 46410 4641.2 46413 46416 46417 46422 46425 46426 46430 79808 79809 79810 79811 79812 7 9813 79820 79836 79837,79838 79839 79840 79847 79848 79849 79850 79851 79852 79872 7 9873 7 9874 7 9875 79876 79877 79884 79885 7 9886 7 9887 7 9888 79908 7 9909 7 9910 7 9911 7 9912 7 991-3 79947 79948 79949 79950 46121 46207 46217 46227 46122 46208 46218 46228 fc14 ** segmentation I fs14 c f24:n 204 208 212 216 220 224 228 232 236 240 244 46123 46209 46219 46229 46126 46127 46128 462 10 46220 46230 * l(SO-85),5(80-1125),12(80-1153) 20351 20352 20353 20354 20355 20356 20357 20358 20359 20360 20361 20362 20363 2 03 64 2 0365 20366 203 67 20368 20369 20370 20371 20372 20373 20374 20375 2037 6 20377 20378 20379 20380 647 0 647 1 647 52 647 53 647 54 647 5 64756 64775 64776 64777 64778 64784 6478 647 86 64787 64 802 64803 64804 64805 64817 64818 64819 64820 64833 6483 4 64852 64853 64866 64867 64887 64888 64902 64903 64918 64919 64935 6493 6 64949 64950 657 0 657 1 657 52 657 53 657 54 657 5 657 56 6577 65776 65777 65778 65784 6 578 6 5786 657 87 65802 65803 65804 65805 65817 65818 65819 65820 65833 6583 4 65852 65853 65866 65867 65887 65888 65902 6 5903 65918 65919 65935 6 593 6 65949 6 5950 6667 66672 66673 66674 6667 66676 66677 66678 66679 66680 66681 66682 66683 66684 66685 66686 66687 66688 66689 66690 66691 66692 66693 66694 66695 66696 66697 66698 66699 66700 66701 66702 66703 66704 66705 66706 667 07 66708 66709 66710 66711 66712 667 13 667 14 66715 667 16 66717 66718 66719 66720 66721 66722 66723 6672 4 6672 66726 66727 66728 66729 66730 66731 66732 66733 6673 4 6673 66736 66737 6673 66739 667 40 667 41 66742 667 43 66744 667 45 66746 66747 667 48 66749 667 0 667 1 667 52 667 53 667 54 667 5 667 56 667 57 667 8 667 59 66760 66761 66762 66763 66764 66765 667 66 66767 66768 66769 66770 66771 66772 66773 6677 4 6677S 66776 66777 66778 667 84 667 5 667 86 66787 667 8 667 89 667 90 66791 667 92 667 93 66794 6679S 66796 66797 66798 667 99 66800 66801 66802 66803 66804 66805 66817 66818 66819 66820 66821 66822 66823 6682 4 66825 66826 66827 66828 6682 9 66830 66831 66832 66833 66834 66852 66853 66854 66855 66856 668 57 66858 66859 66860 66861 66862 66863 66864 66865 66866 66867 66887 66888 66889 66890 66891 66892 66893 66894 66895 66896 66897 66898 66899 66900 66901 66902 6 6 90.3 66918 66919 66 93 O 6693 6 6 94 9 66950 67671 67672 6692 66932 66951 67673 6 7 6 83 67 684 67685 6769 67696 67697 677 07 677 8 67709 66921 66922 66923 66924 66925 66933 6693 4 6693 66936 66952 66953 66954 66955 66956 6767 4 67 67 67 676 67677 67678 67 686 67687 67688 67689 67690 67698 67 699 67700 67701 67702 677 0 677 1 67712 677 13 67714 76 66926 66927 66928 66929 66957 66958 67 679 67 691 67 680 67 681 67 682 67692 67 693 67 694 67703 67704 677 5 677 06 67715 67716 67717 67718 67719 67731 67743 67755 67767 67784 67796 67817 67829 67852 67864 67887 67899 6791.8 67930 67949 f c24 fs24 sd24 67720 67732 67744 67756 67768 67785 67797 67818 67830 67853 67865 67888 67900 67919 67931 67950 67721 67733 67745 67757 67769 67786 67798 67819 67831 67854 67866 67889 67901 67920 67932 67951 67722 67723 67724 67734 6773 67736 677 46 67747 67748 677 8 677 59 67760 67770 67771 67772 6772 6 67727 67728 67729 67730 677 87 677 8 677 99 67800 677 91 677 92 677 93 67794 67795 67803 67 804 67 805 67824 67825 67 826 67827 67828 67 820 67821 67 832 67833 67 855 67 856 6772 67737 677 49 67761 67773 677 89 677 90 67801 67802 67822 67823 67834 67857 67858 67738 67739 677 0 67751 67762 67763 6777 4 67775 67740 67741 67742 677 52 677 53 67 7 54 67764 677 65 677 66 67776 67777 67778 67859 67860 67861 67862 67863 67867 67 890 67 891 67 902 67 903 67892 67893 67894 67895 67896 67897 67898 67921 67922 67923 67924 67925 67926 67927 67928 67929 67 933 67 93 4 67935 67936 67 952 67 953 67954 67955 67956 67957 67958 ** segmentation I ** J(j30-85),5(80-1125),12(80-1153) 204 208 212 216 2,20 224 228 232 236 240 244 (10.76 (74.55 (10.76 (59.17 (59.17 (10.76 (10.76 (59.17 (10.76 (59.17 lOrlO.06) lOr69-68) lOrlO.06) lOr55-31) lOr55.31) lOrlO.06) lOrlO.06) lOr55.31) lOrlO.06) lOr55.31) (35.44 l1r) (35.44 l1r lOrIO.06) lOr55.31) lOr69.68) 5 lOr69.68) 17 lOr55.31) 17 lOr55.31) 74.55 lOr69.68) 74.55 lOr69.68) 59.17 lOr55.31) 10.76 lOrlO 06) (10 (59 (7 4 (7 4 (59 (59 76 17 12.27 l1r) (34.61 l1r) (59.17 (10.76 (59.17 (10.76 (10.76 (59.17 (59.17 (10.76 (74.55 (10.76 300 l1r) (38.00 l1r) lOr 55 3 ) lOr 10 06) lOr 55 3 ) lOr 10 06) lOr 10 0) lOr 55 3 ) lOr 55 3 ) lOr 10. 06) lOr 69 68) lr 10.06) 17.34 l1r) 34.61 l1r) 12.27 l1r) 41 l1r) (8.76 l1r) (8.76 l1r) 12.27 l1r) 35.44 l1r) 876 l1r) 38.00 l1r) (38.00 l1r) 41 l1r) (8.76 l1r) 35.44 l1r) 12.27 l1r) 17.34 l1r) (34.61 l1r) 34.61 l1r) (17.34 l1r) 12.27 l1r) 34.61 l1r) 34.61 l1r) (12.27 l1r) (35.44 l1r) (8.76 l1r) (8.76 l1r) (35.44 l1r) (38.00 l1r) (4.81. l1r) (4.81 l1r) 38.00 l1r) (35.44 l1r) (12.27 l1r) 34.61 l1r) 17.34 l1r) 34.61 l1r) (12.27 l1r) (35.44 l1r) 38.00 l1r) 38.00 l1r) 41 l1r) (8.76 l1r) (8.76 l1r) (4.81 l1r) (38.00 l1r) 38.00 l1r) 12.27 l1r) 35.44 l1r) (8.76 l1r) (4.81 l1r) 41 l1r) (8.76 l1r) 35.44 l1r) (12.27 l1r) (17.34 l1r) (34.61 l1r) (34.61 l1r) 17.34 l1r) 12.27 l1r) 34.61 l1r) 34.61 l1r) (8.76 l1r) (8.76 l1r) 35.44 l1r) 38.00 l1r) (12.2.7 l1r) (3 5.44 l1r) (4.81. l1r) (4 .81 l1r) (38.00 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (2 4. 07 6 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248-076 l1r) (2 48. 07 6 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248 . 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (2 48. 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.,07 6 l1r) (248.076 l1r) (248.076 l1r) (248-076 l1r) (248.076 l1r) (248. 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (2 48. 07 6 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248-076 l1r) (248. 076 l1r) (248.076 l1r) (248.076 l1r) (248-076 l1r) (248.076 l1r) (2 48. 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248. 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (2 48 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (2 48 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (2 4 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (2 48 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (182.31 l1r) (22 6 36 l1r) (98.885 l1r) (208.94 l1r) (98.885 l1r) (226.36 l1r) (182 31 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (2 4 076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (2 48. 07 6 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (4.81 l1r) (4-81 l1r) 77 (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (113.32 l1r) (113.32 l1r) (3.06 l1r) (5.35 l1r) (5.35 l1r) (3.06 l1r) (113.32 l1r) (113.32 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248-076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248-076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (226.36 l1r) (182.31 l1r) (5.35 l1r) (3.06 l1r) (3.06 l1r) (5.35 l1r) (182.31 l1r) (226.36 l1r) (248.076 l1r) (248.076 l1r) (248.076, l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (208.94 l1r) (98.885 l1r) (98.885 l1r) (208.94 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (226.36 l1r) (98.885 l1r) (98.885 l1r) (226.36 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 i1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (182.31 l1r) (5.35 l1r) (5.35 l1r) (182.31 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r) (248.076 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (113.32 l1r) (3.06 l1r) (3.06 l1r) 113.32 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) f248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248-076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248-076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (182.31 l1r) (22:6.36 l1r) (98.885 l1r) (208.94 l1r) (98.885 l1r) (226.36 l1r) (182.31 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248-076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (113.32 l1r) (113.32 l1r) (3.06 l1r) (3.06 l1r) (5.35 l1r) (5.35 l1r) (113.32 l1r) (113.32 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (3.06 l1r) (248-076 l1r) (226.36 l1r) (182.31 l1r) (5.35 l1r) (3.06 llr (5.35 l1r) (182.31 l1r) (226.36 llr (248.076 l1r) (248-076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (208.94 l1r) (98.885 l1r) (98.885 l1r) (208.94 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (226.36 l1r) (98.885 l1r) (98.885 l1r) (226.36 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (182.31 l1r) (5-35 l1r) (5-35 l1r) (182.31 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r) (248.076 l1r) 248-076 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r) (248.076 l1r) (248.076 l1r) (248.076 l1r) (113.32 l1r) (3.06 l1r) (3.06 l1r) 113.32 l1r) 248.076 l1r) 248.076 l1r) 248.076 l1r) (248..076 l1r) 248.076 l1r) 248.076 l1r) 78 248.076 l1r) (248.076 l1r) c f34:n 48195 88750 88775 88787 88802 88814 48199 48115 4119 48135 48139 4815S 48159 48165 48169 88751 88752 887S3 88754 88755 88756 88776 88777 88778 88779 88780 88781 88782 88783 88784 88785 88786 88803 88804 88805 88815 88816 88817 88833 88841 88842 88843 88844 88853 8886.6 88867 88868 88869 88878 88879 88880 88881 88902 88903 88904 88905 88914 88915 88916 88917 fc34 88806 88818 88834 88845 88807 8808 88809 88810 88811 88812 88813 88819 88820 88835 88836 837 88838 88839 88840 88846 88847 88848 88849 88850 88851 88852 88870 88882 88906 88918 88871 88872 88873 88874 88875 88876 88877 88883 88884 88885 88886 88887 88888 88907 88908 88909 88910 88911 88912 88913 88919 88935 88936 88937 88938 88939 88940 88941 88942 88943 88944 88945 88946 88947 88948 88949 88950 89750 89751 89752 89753 89754 89755 89756 89775 89776 89777 89778 89779 89780 89781 89782 89783 89784 89785 89786 89787 89802 89803 89804 89805 89806 89807 89808 89809 89810 89811 89812 89813 89814 89815 89816 89817 89818 89819 89820 89833 89834 89835 89836 89837 89838 89839 89840 89841 89842 89843 89844 89845 89846 89847 89848 89849 89850 89851 89852 89853 89866 89867 89868 89869 89870 89871 89872 89873 89874 89875 89876 89877 89878 89879 89880 89881 89882 89883 89884 89885 89886 89887 89888 89902 89903 89904 89905 89906 89907 89908 89909 89910 89911 89912 89913 89914 89915 89916 89917 89918 89919 89935 89936 89937 89938 89939 89940 89941 89942 89943 89944 89945 89946 89947 89948 89949 89950 ** segmentation II * 280-1120),15(80-890),17(80-892) fs34 204 208 212 216 sd34 (2.81 3r 1.4) (2.81 3r 1.4) (1.415 3r 0326) (1.94 3r 0.97) 1415 3r 0326) (1.94 3r 0.97) 283 3 141) 23 3 141) (3.0 3 1494) 30 3 1494) (30.26 3r 2761) 926 3 084) 115.2 3r 10.52) 22.18 3r2.01) (115.2 3rlO.52) 926 3 084) 30.26 3 2761) 95.16 3r8.67) (95.16 3r 867) 243.21 3r 22.2) 239.63 3r2l.87) 248.075 3r 22.63) (248.075 3r 22.63) 248.075 3r 22.63) 248.075 3r22.63) (248.075 3r 22.63) 239.63 3r 21.87) 243.21 3r 22.2) 95.16 3 867) 3r 867) (243.21 (248.075 (248.075 (248.075 926 3 084) 3r 22.2) 3r 22.63) 3r 22.63) 3r 22.63) 30.26 3r2.761) (248.075 248.075 (248.075 (248.075 3r 3r 3r 3r 22.63) 22.63) 22.63) 22.63) (243.21 3r 22.2) (239.63 3r2l.87) 239.63 3r 21.87) (248.075 248.075 (248.075 (248.075 3r22.63) 3r22.63) 3r22.63) 3r22.63) (30.26 3r2.761) (9.26 3r 0.84) (22.18 3r 2.01) (115.2 3r 10.52) (248.075 3r22.63) (248.075 3r 22.63) (248.075 3r 22.63) (248.075 3r22.63) (248.075 3r 22.63) (248.075 3r 22.63) (248.075 3r22.63) (248.075 3r 22.63) (248.075 3r 22.63) (248.075 3r22.63) (248.075 3r 22.63) (248.075 3r22.63) (248.075 3r22.63) (248.075 3r 22.63) (248.075 3r22.63) (248.075 3r22.63) (248.075 3r 22.63) (115.2 3r 10.52) (22.18 3r 2.01) (9.26 3r 0.84) (115.2 3rlO.52)(248.075 3r22.63) 248.075 3r22.63) (248.075 3r 22.63) 248.075 3r22.63) 248.075 3r22.63) (248.075 3r 22.63) 205.85 3r 18.79) 205.85 3r 18.79) 40.497 3 3692) (140.5 3rl2.8) 40.497 3r3.692) 205.85 3r 18.79) 205.85 3r 18.79) (248.075 3r 22.63) 248.075 3r22.63) 248.075 3r22.63) (248.075 3r 22.63) 248.075 3r22.63) 248.075 3r22.63) (115.2 3rlO.52) 926 3 084) 30.26 3 2761) 239.63 3r 21.87) (248..075 3r 22.63) 248.075 3r22.63) 248.075 3r22.63) (248..075 3r 22.63) (248.07S 3r22.63) (140..5 3rl2.8) 40.497 3r3.692) 40.497 3 3692) 140.5 3r 12.8) (248..075 3r 22.63) 248.075 3r22.63) 248.075 3r22.63) (248.075 3r 22.63) 248.075 3r22.63) 79 95.16 (239.63 3r 21.87) (30.26 3r 2761) 95.16 3r8.67) (248.075 3r 22.63) (248.075 3r 22.63) (40.497 3r3.692) 243.21 3r 22.2) 248.075 3r22.63) 205-85 3r 18.79) 248-075 3r22.63) 40-497 3 3692) 205.85 3r 18.79)(248.075 3r22.63) (248.075 3r 22.63) 248.075 3r22.63) 248.075 3r22.63) (243.21 3r 22.2) 95.16 3r8.67) (30..26 3 2761) (9.26,3r 084) 115.2 3r 10.52) 22.18 3 201) (115.2 3rlO.52) 926 3 084) 30.26 3 2761) 95.16 3 867) (95.16 3r 867) 243.21 3r 22.2) 239.63 3r 21.87) 248.075 3r 22.63) (248.075 3r 22.63) 248.075 3r22.63) 248.075 3r22.63) (248.075 3r 22.63) 239.63 3r 21.87) 243.21 3r 22.2) 95-16 3 867) (95.16 3r 867) 926 3 084) 30.26 3r2.761) 239.63 3r 21.87) (243.21 3r 22.2)(248.075 3r22.63) 248.075 3r22.63) (248.075 3r 22.63) (248.075 3r 22.63) (248.075 3r 22.63) 248.075 3r22.63) 248.075 3r22.63) 248.075 3r22.63) 248.075 3r22.63) 248.075 3r22.63) 248.075 3r22.63) (243.21 3r 22.2) 239.63 3r 21.87) 30.26 3r 2761) (22.18 3 201) 115.2 3rlO.52)(248.075 3r22.63) (248.075 (248.075 (248.075 (246.075 (246.075 (248.075 3r 3r 3r 3r 3r 3r 22.63) 22.63) 22.63) 22.63) 22.63) 22.63) (248.075 3r22.63) (248.075 (248.075 3r22.63) (248.075 (248.075 3r22.63) (248.075 (248.075 3r22.63) (248.075 (248.075 3r22.63) (248.075 (115.2 3r 10.52) (22.18 3r (115.2 3rlO.52)(248.075 3r22.63) 926 3 08'4) 3r22.63) 3r22.63) 3r22.63) 3r22.63) 3r22.63) 2.01) (9.26 3r 0.84). 248.075 3r22.63) (248.075 3r 22.63) 248.075 3r22.63) 248.075 3r22.63) (248.075 3r 22.63) 205.85 3r 18.79) 205.85 3r 18.79) 40.497 3 3692) (140.5 3rl2.8) 40.497 3r3.692) 205.85 3r 18.79) 205.85 3r 18.79) (248.075 3r 22.63) 248.075 3r22.63) 248.075 3r22.63) (248.075 3r 22.63) 248.075 3r22.63) 248.075 3r22.63) (115.2 3rlO.52) 926 3 084) 30.26 3 2761) 239.63 3r 21.87) (248.075 3r 22.63) 248.075 3r22.63) 248.075 3r22.63) (248.075 3r 22.63) 248.075 3r22.63) (140.5 3rl2.8) 40.497 3r3.692) 40.497 3 3692) 140.5 3r 12.8) (248.075 3r 22.63) 248.075 3r22.63) 248.075 3r22.63) (248.075 3r 22.63) 248.075 3r22.63) (239.63 3r 21.87) (30.26 3r 2761) 95.16 3r8.67) 243.21 3r 22.2) (248.075 3r 22.63) 248.075 3r22.63) 248.075 3r22.63) (248.075 3r 22.63) 205.85 3r 18.79) 40.497 3 3692) (40.497 3r3.692) 205.85 3r 18.79)(248.075 3r22.63) (248.075 3r 22.63) (243.21 3r 22.2) c f44:n fc44 248.075 3r22.63) 248.075 3r22.63) 95.16 3r8.67) 48280 48289 48384 48385 48482 48486 48582 48581 48686 48687 49010 49019 49270 49279 49312 49316 49572 49576 49616 49617 49876 49877 47314 47315 47318 47319 47412 47418 47419 47410 47511 47514 47515 47516 47612 47613 47616 47617 47711 47712 47713 47719 47815 47816 47817 47810 ** segmentation III ** 680-1147),19(80-1147),20(80-5237) fs44 204 208 212 216 220 224 228 232 sd44 (9.0 7r9.7) (9.0 (9.0 7r9.7) (9.0 (9.0 7r9.7) (9.0 (1.357 7rO.743) (1.357 7rO.743) 7r 9.7) 7r 97) 7r 97) 1357 7 1357 7 (11.999 8r) (11.999 8r) 11.999 8r) 11.999 8r) 0743) 0743) 12186 7 07798) 12186 7 07798) 80 12186 7r 07798) 12186 7r 07798) (1.357 7rO.743) 1357 7 0743) 12186 7r 07798) 12186 7r 07798) (7.055 7r7.056) 17.31 r) 7055 7 7056) 17.31 r) (7.055 7r7.056) 7055 7 7056) 17-31 r) 17.31 r) (7.055 7r7-056) c f54:n f c54 f s54 sd54 17-31 r) 17.31 r (17.31 Sr) 7055 7 7056) 17.31 r) (17.31 Sr) (17..31 Sr) 7055 7055 7055 7 7 7056) 7056) 7 7055 7 7056) 7055 7 7056) 7056) 17.31 r) 7055 7r7.056) 17.31 Sr) 20151 20152 20153 20154 20155 20156 20157 20158 20159 20160 20161 20162 20163 20164 20165 20166 20167 20168 20169 20170 20171 20172 20173 20174 20175 20176 20177 20178 20179 20180 68750 68751 68752 68753 68754 68755 68756 68775 68776 68777 68778 68779 68780 68781 68782 68783 68784 68785 68786 68787 68802 68803 68804 68805 68806 68807 6808 68809 68810 68811 68812 68813 6881.4 68815 68816 68817 68818 68819 68820 68833 68834 68835 68836 68837 68838 68839 68840 6884 68842 68843 68844 68845 68846.68847 68848 68849 68850 68851 68852 68853 68866 68867 68868 68869 68870 68871 68872 68873 68874 68875 68876 68877 6887 6887 9 68880 68881 68882 68883 68884 68885 68886 68887 68888 68902 68903 68904 68905 68906 68907 68908 68909 68910 68911 68912 68913 68914 68915 68916 68917 68918 68919 68935 68936 68937 68938 68939 68940 68941 68942 68943 68944 68945 68946 68947 68948 68949 68950 697 0 697 1 69752 69753 69754 69755 69756 6977 6977 6 69777 69778 69779 69780 69781 69782 69783 69784 69785 69786 69787 69802 69803 69804 69805 69806 69807 69808 69809 69810 69811 69812 69813 69814 69815 69816 69817 69818 69819 69820 69833 69834 69835 69836 69837 69838 69839 69840 69841 69842 69843 69844 69845 69846 69847 .69848 69849 69850 69851 69852 69853 69866 69867 69868 69869 69870 69871 69872 69873 69874 69875 69876 69877 69878 69879 69880 69881 69882 69883 69884 69885 69886 69887 69888 69902 69903 69904 69905 69906 69907 69908 69909 69910 69911 69912 69913 69914 69915 69916 69917 69918 69919 69935 69936 69937 69938 69939 69940 69941 69942 69943 69944 69945 69946 69947 69948 69949 69950 ** segmentation IV * 41120-1125) 220 224 228 232 236 240 244 (14.9716.47 5rl5.40) (14 97 16 47 (20.3122.35 5r2O.89) (1 69 12 86 (14.9716.47 5rl5.40) (20 3 22 3 (11.6912.86 5r12 02) (20 31 22 3 (11.6912.86 5rl2.02) (11 69 12 86 (14.9716.47 5rl5 40) (1 69 12 86 (14.9716.47 5rl5.40) (20 31 22 3 (11.6912.86 5rl2.02) (20 3 22 3 (14.9716.47 5ri5.40) (11 69 12 86 (11.6912.86 5rl2.02) (14 97 16 47 (27.68 30.46 5r 28.48) 847 932 5rl5.40) (11.69 12.86 5rl2.02) 5rl2.02) (14.97 16.47 5rl5.40) 5r2O.89) (11.69 12.86 5rl2.02) 5r2O.89) (14.97 16.47 5rl5.40) 5rl2.02) (14.97 16.47 5rl5.40) 5rl2.02) (11.69 12.86 5rl2.02) 5r2O.89) (11.69 12.86 5r 20.89) (14.9716.47 5r 12.02) (20.3122.35 5r 15.40) (14.9716.47 5r 8.71) 104.73115.24 (20.0922.1 5r 20.66) 104.73 115.24 5r 107.73) 8479.32 (27.683.0.46 5r28.48) (86.82 95.53 5r 89.3) (86.82 95.53 (220.73 242.89 5r 227.05) 217.3239.12 5r223.52) (225.45 248.08 5r 231.9) (225.45 248.08 5r 231.9) 5rl2.02) 5r 15.40) 5r 20.89) 5r 15.40) 5r 107.73) 5r 871) 5r 89.3) 225.45248.08 5r231.9) (225.45 248.08 5r 231.9) (225.45 248.08 5r 231.9) 217.3 239.12 5r 223.52) (220.73 242.89 5r 227.05) (86.8295.53 5r89.3) 86.82 95.53 5r 89.3) 847 932 5r 871) (27.6830.46 5r28.48) 217.3 239.12 5r 223.52) (220.73 242.89 5r 227.05) (225.45 248.08 5r 231.9) 225.45248.08 5r231.9) 81 (225.45 (225.45 (225.45 (225.45 (225.45 (225.45 (220.73 248.08 248.08 248.08 248.08 248.08 248.08 242.89 5r 5r 5r 5r 5r 5r 5r 231.9) (225.45248.08 231.9) 231-9) (225.45248.08 231.9) 231.9) (225.45248.08 231.9) 227.05) (217.3239.12 5r231.9) 5r231.9) 5r231.9) 5r223.52) (27.6830.46 5r28.48) (8.47 932 5r (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (104.73 115.24 (104.73 115.24 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (171.14 188.32 8.71) 20.0922.1 5r 20.66) 104.73 115.24 5r 107.73) 5r 231.9) 5r 231.9) (225-45248.08 5r231-9) 5r 231.9) 5r 231.9) (225.45248.08 5r231.9) 5r 231.9) 5r 231.9) (225.45248.08 5r231.9) 5r 231.9) 5r 231.9) (225.45248.08 5r231.9) 5r 231.9) 5r 231.9) (225.45248.08 5r231.9) 5r 231.9) 5r 231.9) 5r 107.73) (20.09 22.1 5r 20.66) (8.479.32 5r 8.71) 5r 107.73) 5r 231.9) (225.45248.08 5r231.9) 5r 231.9) 5r 231.9) (225.45248.08 5r231.9) 5r 231.9) 5r 176.04) (171.14 188.32 5r 176.04) (25.1327.65 5r25.85) (107.99 118.82 5r 111.08) (25.13 27.65 5r 25.85) (171.14 188.32 5r 176.04) (171.14 188.32 5r 176.04) (225.45 248.08 5r 231.9) (225.45248.08 5r231.9) (225.45 248.08 5r 231.9) (225.45 248.08 5r 231.9) (225.45248.08 5r231.9) (225.45 248.08 5r 231.9) (104.73 115.24 5r 107.73) (8.47 9.32 5r 8.71) (27.6830.46 5r 28.48) (217.3 239.12 5r 223.52) (225.45 248.08 5r 231.9) (225.45248.08 5r231.9) (225.45 248.08 5r 231.9) (225.45 248.08 5r 231.9) (225.45248.08 5r231.9) (107.99 118.82 5r 111.08) (25.13 27.65 5r 25.85) (25.1327.65 5r25.85) (107.99 118.82 5r 111.08) (225.45 248.08 5r 231.9) (225.45248.08 5r231.9) (225.45 248.08 5r 231.9) (225.45 248.08 5r 231.9) (225.45248.08 5r231.9) (217.3 239.12 5r 223.52) (27.6830.46 5r28.48) 86.82 95.53 5r 9.3) (220.73 242.89 5r 227.05) (225.45 248.08 5r 231.9) 225.45248.08 5r231.9) (225.45 248.08 5r 231.9) (22,5.45 248.08 5r 231.9) 171.14188.32 5r176.04) (25.1327.65 5r25.85) (25.1.327.65 5r25.85) 171.14 188.32 5r 176.04) (225.45 248.08 5r 231.9) (225.45 248.08 5r 231.9) 225-45248.08 5r231.9) (225..45 248.08 5r 231.9) (220..73 242.89 5r 227.05) 86.82 95.53 5r 9.3) (27.6830.46 5r28.48) (8.47 932 5r .71) 104.73 115.24 5r 107.73) .(20.0922.1 5r 20.66) 104.73 115.24 5r 107.73) 847 932 5 871) (27.6830.46 5r28.48) 86.82 95.53 5r 9.3) 86.82 95.53 5r 9.3) (220.73 242.89 5r 227.05) 217.3239.12 5r223.52) (225.45 248.08 5r 231.9) (225.45 248.08 5r 231.9) 225.45248.08 5r231.9) 82 (225.45 248.08 231.9) (225.45 248.08 231.9) 217.3 239.12 223.52) (220.73 242.89 227.05) (86.8295.53 5r89.3) 86.82 95.53 89-3) (8.47 932 (27.6830.46 5r28.48) 217.3 239.12 223.52) (220.73 242.89 Sr 227.05) (225.45 248.08 Sr 231.9) (225-45248.08 5r231.9) (225.45 248.08 Sr 231.S) (225-45248.08 5r231.9) (225.45 248.08 Sr 231.9) (225.45 248.08 Sr 231.9) (225-45248.08 5r231.9) (225.45 248.08 Sr 231.9) (225.45 248.08 Sr 231.9) (225.45248.08 5r231.9) (225.45 248.08 Sr 231.9) (220.73 242.89 Sr 227.05) (217.3239.12 5r223.52) 871) (27.6830.46 5r28.48) (8.47 932 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (104.73 115.24 (104.73 115.24 (225.45 248.08 (225.45 248.08 (225.45 248.08 (225.45 248.08 (171.14 188.32 871) 20.0922.1 20.66) 104.73 115.24 107.73) Sr 231.9) Sr 231.9) (225-45248.08 5r231.9) Sr 231.9) Sr 231.9) (225-45248.08 5r231.9) Sr 231.9) Sr 231.9) (225.45248.08 5r231.9) Sr 231.9) Sr 231.9) (225-45248.08 5r231.9) Sr 231.9) Sr 231.9) (225-45248.08 5r231.9) Sr 231.9) Sr 231.9) Sr 107.73) (20.09 22.1 Sr 20.66) (8.47 9.32 Sr 8.71) Sr 107.73) Sr 231.9) (225.45248.08 5r231.9) Sr 231.9) Sr 231.9) (225.45248.08 5r231.9) Sr 231.9) Sr 176.04) (171.14 188.32 Sr 176.04) (25.1327.65 5r25.85) (107.99 118.82 Sr 111.08) (171.14 188.32 Sr 176.04) (171.14 188.32 Sr 176.04) (22 4 2 48. 08 Sr 23 (225.45 248.08 (225..45 248.08 (225..45 248.08 (104..73 115.24 (217.3 239.12 (225.45 248.08 (225.45 248.08 (225.45 248.08 (107.99 118.82 (107.99 118.82 (225.45 248.08 (225.45 248.08 Sr Sr Sr Sr 9 231.9) 231.9) 231.9) 107.73) 223.52) Sr 231.9) Sr 231.9) Sr 231.9) Sr 111.08) Sr 111.08) Sr 231.9) Sr 231.9) (225.45248.08 5r231.9) (25.13 27.65 Sr 25.85) (225.45248.08 5r231.9) (225.45248.08 5r231.9) (8.47 9.32 Sr 8.71) (225.45248.08 5r231.9) (225.45248.08 5r231.9) (25.13 27.65 Sr 25.85) 225.45 248.08 5r231.9) (86.82 95.53 Sr 89.3) 5r227.05) 5r231.9) (225.45 248.08 5r231.9) 5r231.9) 5r231.9) (171.14 188.32 5r176.04) (25.13 27.65 25.85) (25.1.3 27.65 Sr 25.85) (25.1327.65 (225.45248.08 5r231.9) (217.3 239.12 223.52) (27.68 30.46 Sr 28.48) (220.73242.89 (225.45248.08 (225.45248.08 (225.45248.08 (27.68 30.46 5-r 28.48) (171.14188.32 Sr 176.04) (225.45248.08 5r231.9) (225.45248.08 5r231.9) (225.45 248.08 5r231.9) (225.45248.08 5r231.9) 83 5r25.85) (220.73242-89 5r227.05) c f64:n 46503 46504 46505 46508 46509 46510 46511 46513 46514 46517 46518 46520 46803 46804 46805 46808 46809 46810 46821 46822 46823 46826 46827 46828 47111 47113 47114 47117 47118 47120 fc64 fs64 c f74:n 86.82 95.53 5r segmentation 46521 46811 47103 47121 9.3) 46522 46813 47104 47122 46523 46814 47105 47123 46526 46817 47108 47126 V ** 10(80-872) 46603 46604 46605 46608 46609 46610 46611 46613 46614 46617 46618 46620 46621 46622 46623 46626 46627 46628 ** segmentation VI ** 11(872-1153) fs74 224 228 232 236 240 244 sd74 (1.03 8.35 26.19 27.12 2r 20.3) (0. lr 7.3629.926 2r 7.43) (1.03 835 26.19 27.12 2r 20.3) (0. lr 73629.926 2 743) (1.03 835 26.19 27.12 2r 20.3) (0. 'r 7362 9926 2 743) (1.03 835 (1.03 835 (1.03 835 103 103 835 26.19 27.12 2r 20.3) (0. lr 73629.926 2 743) 103 835 26.19 27.12 2r 20.3) 103 835 26.19 27.12 2r 20.3) 103 835 26.19 27.12 2r 20.3) 44103 44104 44105 44108 44109 44110 44111 44113 44114 44117 44118 44120 44121 44122 44123 44126 44127 44128 45101 45102 45103 45104 45105 45106 45107 45108 45109 45110 45111 45112 45113 45114 45115 45116 45117 45118 45119 45120 45121 45122 45123 45124 45125 45126 45127 45128 45129 45130 fc84 ** segmentation VII ** 13(80-1150) fs84 c f94:n 204 208 212 216 220 224 228 232 236 48105 48109 fc94 ** segmentation VIII ** 16(890-1147) fs94 220 224 228 232 sd94 (6.02 12.0 3r) (6.02 12.0 3r) 44203 44204 44205 44208 44209 44210 44211 44213 44214 44217 44218 44220 44221 44222 44223 44226 44227 44228 44303 44305 44309 44310 44313 44314 44317 44318 44321 44322 44326 44328 45201 45202 45203 45204 45205 45206 45207 45208 45209 45210 45211 45212 45213 45214 45215 45216 45217 45218 45219 45220 45221 45222 45223 45224 45225 45226 45227 45228 45229 45230 45301 45302 45303 45304 45305 45306 45307 45308 45309 45310 45311 45312 45313 45314 45315 45316 45317 45318 45319 45320 45321 45322 45323 45324 45325 45326 45327 45328 45329 45330 47334 47335 47338 47339 47344 47345 47348 47349 47432 47438 47439 47430 47442 47448 47449 47440 47531 47534 47535 47536 47541 47544 47545 47546 47632 47633 47636 47637 47642 47643 47646 47647 47731 47732 47733 47739 47741 47742 47743 47749 47835 47836 47837 47830 47845 47846 47847 47840 fclO4 fslO4 sdlO 835 26.19 27.12 2r 20.3) 103 835 26.19 27.12 2r 20.3) 26.19 27.12 2r 20.3) 26.19 27.12 2r 20.3) 26.19 27.12 2r 20.3) (0. lr 7362 9926 2 743) (0. lr 7362 9926 2 743) c flO4:n 46528 46820 47110 47128 204 208 212 216 220 fc74 c f84:n 46527 46818 47109 47127 segmentation 240 244 3 X ** 8(1150-1125) 82.39 77.02) 455 982 918) 38.282.3977.02) 455 982 918) (38.2 82.39 77.02) (38.282.39 77.02) (38.2 82.39 77.02) (38.282.39 77.02) (38.2 82.39 77.02) (38.282.39 77.02) (4.559..829.18) 38.2 82.39 77.02) (0.130,280.27) (0.13 0.280.27) (0.13 (0.130.280.27) (0.13 0.280.27) (0.13 (0.130.280.27) (0.13 0.280.27) (0.13 (0.290.620.58) (0-29 0.620.58) (8.03 (8.03 17.32 16.18) (0.29 0.62 0.58) (8.03 17.32 16.18) (8.0317.32 16.18) 84 (4.55 9.829.18) (38.282.39 77.02) (38.2 82.39 77.02) (4.55 9.82 9.18) (4.55 9.829-18) (38.282.39 77.02) 0.28 0.27) (0.13 0.280.27) 0.28 0.27) (0.13 0.280.27) 0.28 0.27) (0.13 0.280-27) 17.32 16.18) (5-15 11.11 10.38) (0.29 0.62 0.58) (5.15 11.11 10.38) (5.15 11.11 10.38) 029 062 0.58) (8.03 17.32 16.18) 80317.32 16.18) 029 0620.58) 029 062 058) (8.03 17.32 16.18) (8.0317.32 16.18) 029 0620.58) (5-1511.11 10.38) (8.03 17.32 16.18) (8.0317.32 16.18) (5.15 11.11 10.38) 029 062 0.58) (0.290.620.58) (8.03 17.32 16.18) (5.1 1511-1110.38) (8.0317.32 16.18) (0.290.620.58) 029 0620.58) (0.440.950.88) (2.2 474 443) (2.2 4.74 4.43) (0.44 0.950.88) (2.2 4.74 4.43) (0.071 0.153 0.143) 044 095 0.88) 044 095 0.88) 0071 0153 0143) (2.2 4.744.43) (0.071 0.153 0.143) (0.44 0.95 0.88) (2.2 4.74 4.43) (2.2 4.744.43) (0.440.950.88) (2.2 4.74 4.43) (0.071 0.153 0.143) (0.071 0.153 0.143) (0.44 0.95 0.88) (2.2 4.74 4.43) (2.2 4.74 4.43) (2.2 4.744.43) (0.440-950.88) (0.440.95 0.88) (2.2 4.74 4.43) (2.2 4.744.43) (0.440.950.88) (0.071 0.1530.143) (0.440.950-88) 044 0950.88) (3.11 6.71 6.27) (6.55 14.1213.19) (3.116.71 6.27) (6.55 14.1213.19) (0.15 0.33 0.31) (7.2315.614.58) (0.150.33 0.31) (7.2315.614.58) (3.11 6.71 6.27) (3.11 6.71 6.27) (6.55 14.12 13.19) (6.55 14.1213.19) (0.15 0.33 0.31) (0.15 0.33 0.31) (7.2315.6 14.58) (7.2315.614.58) (3.11 6.71 6.27) (6.55 14.1213.19) (6.55 14-12 13.19) (3.116.716.27) (0.15 0.33 0.31) (7.2315.614.58) (7.23 15.6 14.58) (0.150.330.31) (6.55 14.12 13.19) (7.23 (6.55 (7.23 (3.11 (0.15 c fll4:n fc114 sd114 3116.716.27) 655 14.12 13.19) 3116.716.27) 15.6 14.58) (0.15 033 031) 723 15.614.58) 0150.330.31) 14.12 13.19) 655 14.12 13.19) 311 671 627) 3116.716.27) 15.6 14.58)(7.23 15.6 14.58) (0.1 033 031) 0150.330.31) 6.71 627) 655 14.1213.19) 655 14.12 13.19) 3116.716.27) 0.33 031) 72315.614.58) 723 15.6 14.58) (0.150.330.31). 49300 49309 49602 49606 49906 49907 46703 46704 46721 46722 46911 46913 47203 47204 47221 47222 46705 46723 46914 47205 47223 ** segmentation XI * 0076 0424 0223) (0.076 0424 0223) (0.076 0424 0223) 46708 46726 46917 47208 47226 46709 46727 46918 47209 47227 46710 46728 46920 47210 47228 46711 46903 46921 47211 9872-860),45(5245-5232) 00760.4240.223) 46713 46904 46922 47213 46714 46905 46923 47214 fs114 46717 46908 46926 47217 46718 46909 46927 47218 224 228 00760.4240.223) 00760.4240.223) (2.53.580.27) 114 1650.27) 25 358 027) 114 165 027) (2.53.580.27) 25 358 027) 114 165 027) 253.58 027) (2.53,.580.27) 25 358 027) 253.580.27) 1141.65 027) (2.53.580.27) 25 358 027) 114 165 027) 253.58 027) (1.14 165 027) 25 3580.27) (6.02 864 0.8) 31 4570.74) 602 864 0.8) 31 457 074) (6.028.640.8) (6.028.640.8) (3.184.570.74) (6.02 8.64 0.8) (6.028.640-8) (6.028.640.8) (6.028.640.8) (3.18 4.570.74) (6.028.640.8) (6.028.640.8) (3.184.570.74) (6.02 8.64 0.8) (3.184.570.74) 602 864 0.8) (6.459.250.5) (6.459.250.5) (6.459.250.5) (6.459.250.5) (2.633.770.6) c fl24:n fc124 sd124 (2.633.770.6) (6.459.250.5) (6.459.250.5) (6.459.250.5) (6.459.250.5) (6.459.250.5) (2.633.770.6) (6.459.250.5) (2.633.770.6) (2.63 (6.45 (2.63 (6.45 3.770.6) 9.250.5) 3.770.6) 9.250.5) 49030 49039 49332 49336 49636 49637 49070 49079 49100 49109 49372 49376 49402 49406 49676 49677 49706 49707 segmentation XII ** 22(5233-5234),26(5240-5241) 01043 00904) 010430.0904) (0.1043 00904) 010430.0904) (0.1043 00904) 010430.0904) 85 fs124 232 46720 46910 46928 47220 (l.l.le-4 9.6e-5) 1lle-4 9.6e-S) 009 0078) 009 0078) 1lle-4 (l.l.le-4 9.6e-5) 009 0078) 009 0078) 1.11e-4 9.6e-5) 1lle-4 (0.09 0078) 009 0078) c fl34:n 9.6e-5) 9.6e-5) 49110 49119 49150 49159 49180 49189 4941.2 49416 49452 49456 49482 49486 49716 49717 49756 49757 49786 49787 fc134 ** segmentation XIII ** 29(5243-5244),33(5250-5251) fs134 sd134 c fl44:n 220 0032 0163) 0032 0163) (3.39e-5 1.73e-4) (3.39e-5 1.73e-4) 00275 01405) (0.02750.1405) (0.032 0163) 0032 0163) (3.39e-5 1.73e-4) (3.39e-5 1.73e-4) 00275 0.1405) 002750.1405) (0.032 0163) 0032 0163) (3.39e-5 1.73e-4) (3.39e-5 1.73e-4) 00275 0.1405) 002750.1405) 49190 49199 49230 49239 49260 49269 49492 49496 49532 49536 49562 49566 49796 49797 49836 49837 49866 49867 fc144 ** segmentation XV** 36(5253-5254),40(5260-5261) fs144 sd144 212 0187 7.7e-3) (0.1877.7e-3) (1.987e-4 8.26e-6) (1.987e-48.26e-6) (0.161 0007) 0161 0007) (0.187 7.7e-3) (0.1877.7e-3) (1.987e-4 8.26e-6) (1.987e-48.26e-6) (0.161 0007) 0161 0007) (0.187 7.7e-3) (0.1877.7e-3) (1.987e-4 8.26e-6) (1.987e-48.26e-6) (0.161 0007) 0161 0007) c fl54:n 49280 49289 49582 49586 49886 49887 fc154 ** segmentation XVI ** 43(80-5252) fs154 204 208 sd154 (0.424 Ir 0.069) c fl64:n (0.424 lrO.069) (0.424 lr 0069) (0.424 lr 0069) 0424 lrO.069) 0424 lrO.069) 49290 49299 49592 49596 49896 49897 fc164 ** segmentation XVII ** 44(5255-5242) fs164 sd164 216 (0.3649 0.3578) (0.36490.3578) (0.3649 03578) (0.3649 03578) 036490.3578) 036490.3578) 86 APPENDIX PROCESSING PROGRAMS The following program and file listings are given in this Appendix xcgOln.f incore flux, tally processing program xcgln.f incore homogenized cross section processing program prohxln.f out of core flux and cross section processing program prohx2n.f version of prohxln.f for the cells below surface 5 sibel.f the program written to prove accuracy of processing programs rs___ the results of sibel.f 87 Program : xcgOln.f character*8 kodver character*19 probid character*79title character*4ntalvals character*5 tallykcode character*2fdusmc,,et character*3 tfc character*75 c fcomment integer indllupflindfnff integer rnrpbnameptypecellntallyn real cellvxdatatrf dimension ebin(3) dimension celln(62),tallyn(35),xkeff(3) dimension tf(8) c common/datv/cellv(3659),indl(3659,5),lupfl(2),indf common/datc/nff(3S) common/datx/xdata(2,35,3,5,14,62) common/rslt/trf(2,24,12,3) c c xdata(2,35 3 514,70) c c c c (2, nt, ne, nm, ns, n f nt tally no : ne energy bin no. rim multiplier no. c c ns nf c trf segment no. cell no. 2, 24, 12, 3, 5) c (i, ni, ns, ne, nm) c c c ni : triangle no open(unit=13,file=lmcxllform=lformattedl,status=loldl) open(unit=19,file=lvol7l,form=lformattedl,status=loldl) open(unit=llfile=lxcllform=lformattedl,status=lunknown') open(unit=20,file=ltrrllform=lformattedl,status=lunknown') open(unit=22,file=ltrfllform=lformattedl,status=lunknown') c c Start to read cell volume data from vol, file c ind=O do 101 i=1,3659 read(19,103)(indl(i,k),k=1,2),cellv(i),(indl(i,i),j=3,5) 103 101 format(i6,xi6,1pe13.5,3(xi2)) continue 501 format(2a8,a19,i5,i11,i15) 502 format (1x, a7 9) 503 format(aCi6) 600 format(16i5) read(13,501)kod,ver,probid,knod,nps,rnr write(11,5011)kod,ver,probid,knod,nps,rnr 5011 format(ITally file:'/,Imcxll,2x,2a8,al9,i5,illil5) c read(13,502)title c read(13,503)ntalnt c read(13,600)(ta1lyn(i),i=1,nt) c c ***** Start ally loop c 88 do 100 n=lnt read(13,504)tallypbnameptype 504 format(a5,2i5) read(13,505)fcomment 505 format(5xa75) 506 format(a2,i8) 507 format(11i7) read(13,506)fnff(n) nf=nff(n) read(13,507)(ce1ln(i),i=1,nf) read(13,506)didumm read(13,506)uidumm read(13,506)sns read ( 3, 5 6 m, nm if(nm.'eq.O)rim=l read(13,506)cnc if(nc.eq.O)nc=l 508 509 format(a2,iBi4) format(lp6el3.5) 510 format(a4) read(13,506)ene read(13,509)(ebin(i),i=1,ne) read(13,506)tidumm read(13,510)vals c c Read list of tally/error c data pairs read(13,511)(((((xdata(it,n,ie,im,is,ic),it=1,2), x ie=lne),im=lnm),is=lns),ic=lnf) 511 1025 format(4(1pe13.5,Opf7.4)) format(i3,xi5,Ip1Oe1O.3) c c Read tally c fluctuation data read(13,512)tfc,nfc,(jtf(i),i=1,8) 512 format(a3,i5,8i8) do 150 j=lnfc read(13,513)npsxtallyxerrfom 513 150 format(i11,1p3e13-5) continue c c ***** End of tally 100 continue loop c c Read kcode data c read(13,3000,end=999)kcode,ncycle 3000 format(a5,i5) c do 200 ncy=1,ncycle read(13,3010,end=998)(xkeff(k),k=1,3),dummyl,dummy2 200 continue 3010 format(lp5el2.5) c 998 continue 999 continue c c • Processing xdata and frac and cellv to get triangle • call parameters (imatl1w,1upititnca11n) sections c c • • • • imat: l1w lup it material number to fetch from cell volume array starting line number cell volume to be found the array final line number to find cell volume order of tally in mcx file no. iu 89 • itn problem number of tally(only used in if statements) calln: variable to count no of calls from main • c indf-1 call flux(4,1,152,3,24,1) call. call. call. call call. call. call call flux(1,1,152,4,34,2) flux(2,1,152,5,44,3) flux(0,153,511,1,4,4) flux(5,155,514,2,14,5) flux(4,292,510,12,124,7) flux(1,292,510,13,134,B) flux(2,292,510,14,144,9) flux(7,2,0,18,194,10) do ilk=1,2 write(22,556)(((trf(ilk,i,jk),k=1,3),j=1,12),i=1,24) 555 556 format(lp5el3.5) format(lp3el3.5) end do c stop end c------------------------------------------------------------------------c SUBROUTINE FOR FLUX CALCULATION c------------------------------------------------------------------------subroutineflux(imatllwlupititnjale) c integer indllupflindfnff real cellvxdatatrf common/datv/cellv(3659),indl(3659,5),lupfl(2),indf common/datc/nff(35) common/datx/xdata(2,35,3,5,14,62) common/rslt/trf(2,24,12,3) c I write(11,1001)imat,llw,lup,it,itn,jale 1001 format(5xlflux ,6i8) c ic=O idmat=1 iflagd=O iflags=O nseg=12 nm=3 c c --- check for dummyelements that have 14 segments, if(itn.ge.4.and.itn.le.14)iflagd=1 ignore 1st last c c --- check for fuel materials c if(itn.eq.24.or.itn.eq.124)then lupfl(indf)=lup indf=indf+l endif c c --- check for aluminum tallies c to separate a1200, a1300, and a1600 if(itn.eq.44.or.itn.eq.144)idmat=3 c c --c check for tally 4 and 14 to separate 2 cells if(itn.eq.4.or.itn.eq.14)idmat=2 c c --- check for imat=7 to separate the cells of tally 194 c if(imat..eq.7)idmat=llw c 90 c llup=lup lllw=llw c c do loop to separate cells in same tally c do 500 jj=lidmat if(imat.eq.7)then lup=lupfl(jj) l1w=1up-12 if(ii.eq.2)ic=4 else if(idmat.eq.3)then if(jj,.eq.l)then imat=2 endif if(ii.eq-2)then imat=3 ic=30 endif if(jj.eq.3)then imat=6 ic=60 endif endif c c c if tally4 and 14 then take llw of both cells from call parameters if(itn.eq.4)then if(ii.eq.l)then lup=lllw+l endif if(ii.eq.2)then ic=1 llw=llup lup=llup+2 endif endif if(itn.eq.14)then if(jj.eq.l)then lup=lllw+4 endif if(ii.eq.2)then ic=4 llw=llup lup=llup+9 endif endif endif c ----------------------------------------------------------------------CALCULATION OF TRIANGLE FLUX c TOTALS c -----------------------------------------------------------------------do 410 ii=llwlup imt=indl (ii, 5) if(imat.eq.imt)then if(ind.eq.O)then ic=ic+l ni 1=indl (i i, 4) ni2=indl(ii+1,4) ni3=indl(ii+2,4) nct=indl(ii,3) do 400 ie=1,3 imn=1 do 400 is=lnseg c ignore lst segment ---------------------- iss=is 91 ind=O isg=is+iflagd c fmm = total cellv segment volume fmm=12. if(iflags.eq.l)then iss=iss+5 fmm=6.4357647 if(isg.eq.1)fmm=14.768897 endif if(iflags.eq.2)then fmm=5.5642353 if(isg.eq.6)fmm=9.8615507 endif cvl=cellv(ii)/fmm cv2=cellv(ii+l)/fmm cv3=cellv(ii+2)/fmm if(nct.eq.O)then c x x trf(l,nil,iss,ie)=trf(l,nil,iss,ie) +xdata(litieimnisgic)*cvl trf(2,nil,iss,ie)=trf(2,nil,iss,ie)+ (xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cvl)**2 ind=O c elseif(nct.eq.l)then c x x trf(.lnil,iss,ie)=trf(l,nil,iss,ie) +xdata(litieimnisgic)*cvl trf(l,ni2,iss,ie)=trf(l,ni2,iss,ie) +xdata(litieimnisgic)*cv2 x trf(2,nil,iss,ie)=trf(2,nil,iss,ie)+ (xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cvl)**2 trf(2,ni2,iss,ie)=trf(2,ni2,iss,ie)+ x (xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cv2)**2 c ind=1 elseif(nct.eq.2)then c x x x x x x trf(l,nil,iss,ie)=trf(l,nil,iss,ie) +xdata(litieimnisgic)*cvl trf(l,ni2,iss,ie)=trf(l,ni2,iss,ie) +xdata(litieimnisgic)*cv2 trf(l,ni3,iss,ie)=trf(l,ni3,iss,ie) +xdata(litieimnisgic)*cv3 trf(2,nil,iss,ie)=trf(2,nil,iss,ie)+ (xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cvl)**2 trf(2,ni2,iss,ie)=trf(2,ni2,iss,ie)+ (xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cv2)**2 trf(2,ni3,iss,ie)=trf(2,ni3,iss,ie)+ (xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cv3)**2 ind=2 endif imark=ii+nct 400 continue else ind=ind-1 endif endif 410 500 600 if(imark.eq.lup.and.jj.eq.2)goto continue continue continue 600 return end 92 c Program : xcgln.f character*8 kodver character*19 probid character*79title character*4ntalvals character*5 tallykcode character*2 fdusmcet character*3 tfc character*75 c fcomment integer indllupflindfnff integer rnrpbnameptypecellntallyn real cellvxdatatrr dimension ebin(3) dimension celln(62),tal1yn(35),xkeff(3) dimension jtf(8) c common/datv/cellv(3659),indl(3659,5),lupfl(2),indf common/datc/nff(35) common/datx/xdata(2,35,3,5,14,62)common/rslt/trr(2,24,12,3,5) c c xdata(2,35, 3, 5,14,70) c c c c (2 nt, ne I ran, ns, nf nt tally no : ne energy bin no. nm multiplier no. c c ns nf c segment no. cell no. trr(2,24,12, c c i c ni c c 3, 5) (ininsnenm) value, stdev pair triangle no open(unit=13,file=lmcxllform=lformatted',status='old') open(unit=19,file=lvol7l,form=lformatted',status='old') open(unit=llfile=lxcl',form='formattedl,status='unknown') open(unit=20,file=ltrrllform=lformattedl,status=lunknown') c c Start to read cell volume data from 'vol' file c ind=O 103 101 do 101 i=1,3659 read(19,103)(indl(i,k),k=1,2),cellv(i),(indl(i,j),j=3,5) format(i6,xi6,1pel3.5,3(xi2)) continue 502 format(lxa79) 503 format(aCi6) 600 format(16i5) read(13,501)kod,ver,probid,knod,nps,rnr 501 format(2a8,a19,i5,il1,i15) write(11,5011)kod,ver,probid,knod,nps,rnr 5011 format(ITally file:,/,Imcxll,2x,2a8,al9,i5,illil5) c read(13,502)title c read(13,503)ntalnt c read(13,600)(tallyn(i),i=lnt) c c ***** Start tally loop c do 100 n=lnt read(13,504)tallypbnameptype 504 format (a5, 2 i5) read(13,505)fcomment 505 format(5xa75) read(13,506)fnff(n) 93 506 nf =nf f (n) format(a2,i8) 507 format (1 1 i7) read(13,507)(celln(i),i=1,nf) read(13,506)didumm read(13,506)uidumm read(13,506)sns read(13,506)mnm if(nm.eq.o)nm=l read(13,506)cnc if(nc-eq.O)nc=l 508 509 format(a2,i8,i4) format(lp6e13.5) read(13,506)ene read(13,509)(ebin(i),i=1,ne) read(13,506)tidumm read(13,510)vals 510 format(a4) c c Read list of tally/error c data pairs read(13,511)(((((xdata(it,n,ie,im,is,ic),it=1,2), 511 1025 x ie=lne),im=lnm),is=lns),ic=lnf) format(4(1pe13.5,Opf7.4)) format(i3,xi5,1p1Oe1O.3) c c Read tally c 512 fluctuation data read(13,512)tfc,nfc,(jtf(i),i=1,8) format(a3,i5,8i8) do 150 j=lnfc read(13,513)npsxtallyxerrfom 513 150 format(illlp3e13.5) continue c c ***** End of tally 100 continue loop c c Read kcode data c read(13,3000,end=999)kcode,ncycle 3000 format(a5,i5) c do 200 ncy=1,ncycle read(13,3010,end=998)(xkeff(k),k=1,3),dummyl,dummy2 200 continue 3010 format(lp5el2.5) c 998 continue 999 continue c c • Processing xdata and frac and cellv to get triangle • call parameters (imatllwlupititncalln) sections c c • • • • • • imat: llw lup it itn calln: material number to fetch from cell volume array starting line number cell volume to be found the array final line number to find cell volume order of tally in mcx file no. iu problem number of tally(only used in if statements) variable to count no of calls from main c indf=1 call tri(4,1,152,6,64,1) 94 call tri(1,1,152,7,74,2) call tri(2,1,152,8,84,3) call tri(0,153,511,9,94,4) call call call call call tri(5,155,158,10,104,5) tri(5,514,521,11,114,6) tri(4,292,510,15,164,7) tri(1,292,510,16,174,8) tri(2,292,510,17,184,9) call tri(7,2,0,19,204,10) do ilk=1,2 write(20,555)((((trr(ilk,ijk,l),1=1,5),k=1,3),j=1,12),i=1,24) 555 format(lp5e13.5) end do c stop end subroutinetri(imatl1w,1upititnncall) c integer indllupflindfnff real cellvxdatatrr common/datv/cellv(3659),indl(3659,5),lupfl(2),indf common/datc/nff(35) common/datx/xdata(2,35,3,5,14,62) common/rslt/trr(2,24,12,3,5) c write(11,1001)imat,llw,lup,it,itn,jale 1001 format(5xltri ,6i8) c ic=O idmat=1 iflagd=O iflags=O nseg=12 nm=3 c c --- check for dummy elements that have 14 segments, if(itn.ge.94.and.itn.le.114)iflagd=1 ignore 1st last c c --- check for fuel materials to assign no. of multipliers c if(itn.eq.64.or.itn.eq.164)then nm=5 lupfl(indf)=lup indf=indf+l endif c c --c check for aluminum tallies to separate a1200, a1300, and a1600 if(itn.eq.84.or.itn.eq.184)idmat=3 c c --- check for tally 94 to separate 2 cells c if(itn.eq.94)idmat=2 c c --- check for imat=7 to separate the cells of tally 204 c c if(imat.eq.7)idmat=llw llup=lup lllw=llw c c do-loop to separate cells in same tally c do 500 jj=lidmat if(imat.eq.7)then lup= lupf 1 (j j ) 95 c llw=lup-12 else if(jj.eq-2)ic=4 if(idmat.eq.3)then if(j1j.eq.1)then . imat=2 endif if(ii-eq-2)therk imat=3 ic=30 endif if(ji.eq.3)then imat=6 ic=60 endif endif c c if tally94 then take llw of both cells from call parameters c if(itn.eq.94)then if(jj-eq.1)then lup=lllw+l endif if(ji.eq.2)then ic=1 llw=llup lup=llup+2 endif endif endif c ----------------------------------------------------------------------c CALCULATION OF TRIANGLE REACTION RATE TOTALS c -----------------------------------------------------------------------ind=O do 410 ii=llwjup imt=indl(ii,5) if(imat.eq.imt)then if(ind.eq.O)then ic=ic+l nil=indi(ii,4) ni2=indl(ii+1,4) ni3=indl(ii+2,4) nct=indl(ii,3) do 400 ie=1,3 do 400 im=lnm do 400 is=lnseg • ignore 1st segment ---------------------- iss=is isg=is+iflagd • fmm total cellv segment volume fmm=12. if(iflags.eq.1)then iss=iss+5 fmm=6.4357647 if(isg.eq.1)fmm=14.768897 endif if(iflags.eq.2)then fmm=5.5642353 if(isg.eq.6)fmm=9.8615507 c fuel multiplier endif adjustment imn=iM if(imat.eq.4.and.im.le.3)imn=im+2 if(imat.eq.4-and.im.gt.3)imn=im-3 96 cvl=cellv(ii)/fmm cv2=cellv(ii+l)/fmm cv3=cellv(ii+2)/fmm if(nct.eq.O)then c x x trr(.Inil,iss,ie,im)=trr(l,nil,iss,ie,im) +xdata(litieimnisgic)*cvl trr(2,nil,iss,ie,im)=trr(2,nil,iss,ie,im)+ (xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cvl)**2 c ind=O elseif(nct.eq.l)then c x x x x trr(l,nil,iss,ie,im)=trr(l,nil,iss,ie,im) +xdata(litieimnisgic)*cvl trr(l,ni2,iss,ie,im)=trr(l,ni2,iss,ie,im) +xdata(litieimnisgic)*cv2 trr(2,nil,iss,ie,im)=trr(2,nil,iss,ie,im)+ (xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cvl)**2 trr(2,ni2,iss,ieim)=trr(2,ni2,iss,ie,im)+ (xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cv2)**2 c ind=1 elseif(nct.eq.2)then c x x x x x trr(l,nil,iss,ie,im)=trr(l,nil,iss,ie,im) +xdata(litieimnisgic)*cvl trr(l,ni2,iss,ie,im)=trr(l,ni2,iss,ie,im) +xdata(litieimnisgic)*cv2 trr(l,ni3,iss,ie,im)=trr(l,ni3,iss,ie,im) +xdata(litieimnisgic)*cv3. trr(2,nil,iss,ie,im)=trr(2,nil,iss,ie,im)+ (xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cvl)**2 trr(2,ni2,iss,ieim)=trr(2,ni2,iss,ie,im)+ (xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cv2)**2 trr(2,ni3,iss,ieim)=trr(2,ni3,iss,ie,im)+ x (xdata(l,it,ie,imn,isg,ic)*xdata(2,it,ie,imn,isg,ic)*cv3)**2 c ind=2 endif imark=ii+nct 400 continue else ind=ind-1 endif endif 410 500 600 if(imark.eq.lup.and.jj.eq.2)goto continue continue continue 600 return end Program : prohxln.f program prohx1n c This program processes mctal file of input file outhx2 character*8 kodver character*19 probid character*79title character*4ntalvals character*5 tallykcode character*2 fdusmcet 97 character*3 tfc character*75 c fcomment integer tal1yn(56),pbnameptypenff(90) dimensionxkeff(3),ebin(3),jtf(8) c dimension celln(10000),fldat(2,3,12,5000),rrdat(2,3,5,12,5000) dimensiontrf(2,40,20,12,3),trr(2,40,20,12,3,5) dimension nj(9),kl(9),k2(9),jj(9,32),il(9,32),i2(9,32),nseq(9,32) itri(40,20) dimension cvo1(5,2166),no(5,2166),nom(5) dimension cvol2(5,2166),no2(5,2166),nom2(5) dimension voltr(40,20,12,3) dimension flx(40,20,12,3),totxs(40,20,12,3),absxs(40,20,12,3) dimension elsct(40,20,12,3),diffc(40,20,12,3),fisnu(40,20,12,3) dimension fisxs(40,20,12,3) c rea1*8 stflx,sttxs,staxs,stels,stfxs,stfnu dimension stflx(40,20,12,3),sttxs(40,20,12,3),staxs(40,20,12,3) dimension stels(40,20,12,3),stfxs(40,20,12,3),stfnu(40,20,12,3) c open(unit=llfile=lhxln.oul,form=lformattedl,status=lunknown') open(unit=12,file='inpt',form='formattedl,status=loldl) open(unit=13,file=lmcxohl,form--'formattedl,status=loldl) open(unit=14,file=ltlistall,form='formatted',status=lunknown') open(unit=15,file=ltri6OO.l',form='formattedl,status=loldl) open(unit=16,file='vale',form='formattedl,status=loldl) open(unit=17,file='vale2l,form=lformattedl,status=loldl) open(unit=18,file=ltlista3l,form='formatted',status=lold') open(unit=20,file=ldebug.ol,form='formattedl,status='unknown') c • Sequential reading from mctal file, first fluxes then reaction rates • After data has been read subroutines process the data and add it to the • triangle totals of fluxes or reaction rates. write(11,10) 10 format(///5x,'PROHX1.F - AN MCNP TALLY PROCESSING PROGRAM',//) c c Reading the general info about tallies c (not to be processed) read(13,501)kod,ver,probid,knod,nps,rnr 501 format(2a8,a19,i5,i11,i15) 502 format(lxa79) write(11,5011)kod,ver,probid,knod,nps,rnr 5011 format('Tally file:,/,'mcxohl,2x,2a8,al9,i5,illil5) c read(13,502)title write(11,502)title c c nt=56 read(13,503)ntalnt 503 format(a5,i5) 600 format (16i5) c read(13,600Htallyn(i),i=1,nt) c c ***** Start tally loop c nfkeepl=l nfkeep2=0 nfkeep3=1 nfkeep4=0 do 100 n=lnt read(13,504)tallypbnameptype 504 format(a5,2i5) 98 dimension read(13,505)fcomment 505 506 format(5xa75) read(13,506)fnff(n) format(a2,A) nf=nff(n) if(n.le.17)then nfkeepl=nfkeep2+1 nfkeep2=nfkeep2+Df endif if(n.gt.17)then nfkeep3=nfkeep4+1 nfkeep4=nfkeep4+nf endif if(n.le-17)read(13,507) (celln(i),i=nfkeeplnfkeep2) if(n.gt.17)read(13,507) (celln(i),i=nfkeep3,nfkeep4) 507 format(11i7) read(13,506)didumm read(13,506)uidumm read(13,506)sns if(ns.eq.O)ns=l read(13,506)mnm if(nm.eq.O)nm=l 509 read(13,506)cnc if(nc.eq.O)nc=l read(13,506)ene read(13,509)(ebin(i),i=1,ne-1) format(lp6el3.5) read(13,506)tidumm read(13,510)vals 510 format(a4) c c Readlist of tally/error data pairs c if(n.le.17)then read(13,511)((((fldat(it,ie,is,ic),it=1,2), 511 x ie=1,3),is=lns),ic=nfkeepl,nfkeep2) format(4(1pe13.5,Opf7.4)) endif if(n..gt.17)then read(13,511)(((((rrdat(it,ie,im,is,ic),it=1,2), x ie=1,3),im=lrim),is=lns),ic=nfkeep3,nfkeep4) endif c c Read tally fluctuation c data read(13,512)tfc,nfc,(jtf(i),i=1,8) 512 format(a3,i5,8i8) do 150 j=lnfc read(13,513)npsxtallyxerrfom 513 150 format(illlp3el3.5) continue c c ***** End of tally loop 100 continue c c Read kcode data c read(13,3000,end=999)kcode,ncycle 3000 format(a5,i5) do 200 ncy=lncycle read(13,3010,end=999)(xkeff(k),k=1,3),dummyl,dummy2 99 200 continue 3010 format(lp5el2.5) 999 continue c c Multiplier sequence change for detector uranium coatings c do 778 ic=1,2166 if((ic.ge. 213.and.ic.le. 248).or. x (ic-ge.2107.and.ic.le.2112).or. x (ic.ge.2125.and.ic.le.2130).or. x (ic.ge.2143.and.ic.le.2148))then do 777 it=1,2 do 777 ie=1,3 do 777 is=1,12 xxl=rrdat(itielisic) 777 continue 778 continue xx2=rrdat(itie,2,isic) rrdat(it,ielis,ic)=rrdat(it,ie,3,is,ic) rrdat(it,ie,2,is,ic)=rrdat(it,ie,4,is,ic) rrdat(it,ie,3,is,ic)=rrdat(it,ie,5,is,ic) rrdat(itie,4,isic)=xxl rrdat(itie,5,isic)=xx2 endif c c Read segment volume data from vale c do 413 ill=1,2166 read(16,1(2i6,5(lpel3.5,i3))I)ic,noc,cvol(l,ill),no(l,ill), x cvol(2,ill),no(2,ill),cvol(3,ill),no(3,ill),cvol(4,ill), x no(4,i.11),cvol(5,ill),no(5,ill) 413 continue c same for trr from vale2 do 531 ill=1,2166 read(17,1(2i6,5(lpel3.5,i3))I)ic,noc,cvol2(l,ill),no2(l,ill), x vol2(2,ill),no2(2,ill),cvol2(3,ill),no2(3,ill),cvol2(4,ill), no2(4,ill),cvol2(5,ill),no2(5,ill) 531 continue c c Read cell number to triangle number conversion data from inpt c read(12,301) (nj(n),n=1,9) read(12,301) (kl(ik),ik=1,9) read(12,301) 301 k2(ik),ik=1,9) format(9i3) do 101 ii=1,9 read(12,302)(jj(iiij),ij=lnj(ii)) 101 continue do 102 ii=1,9 read(12,302)(il(iiiin),iin=lnj(ii)) read(12,302)(i2(iiiin),iin=lnj(ii)) 302 102 format (23i3) continue do 103 isq=1,9 read(12,303) (nseq(isqiin),iin=1,nj(isq)) 303 103 format(14i5) continue do 110 ng=1,9 do 1 1 0 nn= 1, n (ng) do 110 ie=1,2 do 110 i=il(ngnn),i2(ngnn) do 110 k=kl(ng),k2(ng),-l 100 x j=jj (ng,-) ic=nseq(ngnn)+i-il(ngnn) is=kl(ng)+l-k nom(1)=no(1,ic) nom(2)=no(lic)+no(2,ic) nom(3)=no(l,ic)+no(2,ic)+no(3,ic) nom(4)=no(l,ic)+no(2,ic)+no(3,ic)+no(4,ic) nom(5)=no(l,ic)+no(2.,ic)+no(3,ic)+no(4,ic)+no(5,ic) if(is.le.nom(1))cvlm=cvo1(1,ic) if(is.gt.nom(l).and.is.le.nom(2))cvlm=cvol(2,ic) if(is.gt.nom(2).and.is.le.nom(3))cvlm=cvol(3,ic) if(is.gt.nom(3).and.is.le.nom(4))cvlm=cvol(4,ic) if(is.gt.nom(4).and.is.le.nom(5))cvlm=cvol(5,ic) x 110 trf(l,ijk,ie)=trf(l,i,jk,ie)+fldat(l,ie,is,ic)*cvlm voltr(ijk,ie)=voltr(ijk,ie)+cvlm trf(2,ijk,ie)=trf(2,ijk,ie)+(fldat(l,ie,is,ic)*cvlm* fldat(2,ieisic))**2 continue c c the same thing for trr data from vale2 and inpt c read(12,301) (nj(n),n=1,9) read(12,301) (kl(ik),ik=1,9) read(12,301) (k2(ik),ik=1,9) do 191 ii=1,9 191 continue read(12,302)(jj(iiij),ij=1,nj(ii)) do 192 ii=1,9 read(12,302)(i1(iiiin),iin=Inj(ii)) read(12,302)(i2(iiiin),iin=1,nj(ii)) 192 continue do 193 isq=1,9 read(12,303) (nseq(isqiin),iin=1,nj(isq)) 193 continue do 111 ng=1,9 do 1 1 1 nn= 1, nj (ng) do 111 ie=-1,2 do 111 i=il(ngnn),i2(ngnn) do 111 k=kl(ng),k2(ng),-l ic=nseq(ngnn)+i-il(ngnn) is=kl(ng)+l-k nom2(1)=no2(lic) nom2(2)=no2(lic)+no2(2,ic) nom2(3)=no2(l,ic)+no2(2,ic)+no2(3,ic) nom2(4)=no2(l,ic)+no2(2,ic)+no2(3,ic)+no2(4,ic) nom2(5)=no2(l,ic)+no2(2,ic)+no2(3,ic)+no2(4,ic)+no2(5,ic) if(is.le.nom2(l))cvlm=cvol2(l,ic) if(is.gt.nom2(l).and.is.le.nom2(2))cvlm=cvol2(2,ic) if(is.gt.nom2(2).and.is.le.nom2(3))cvlm=cvol2(3,ic) if(is.gt.nom2(3).and.is.le.nom2(4))cvlm=cvol2(4,ic) if(is.gt.nom2(4).and.is.le.nom2(5))cvlm=cvol2(5,ic) do 111 im=1,5 trr(l,i,jk,ie,im)=trr(l,i,jk,ie,im)+rrdat(l,ie,im,isic)*cvlm trr(2,i,jk,ieim)=trr(2,i,jk,ie,im)+(rrdat(l,ie,im,is,ic)* x 111 continue cvlm* rrdat(2,ieimisic))**2 c c Read the rest of the conversion data for flux from tlistal c do 312 loop=1,846 read(14,1(i6,i6,4i3,i6)',end=313)isqn,ncl,i,jktopkbot,idm2 nom(l)=no(lic) nom(2)=no(lic)+no(2,ic) 101. ic=isqn nom(3)=no(l,ic)+no(2,ic)+no(3,ic) nom(4)=no(l,ic)+no(2,ic)+no(3,ic)+no(4,ic) nom(5)=no(l,ic)+no(2,ic)+no(3,ic)+no(4,ic)+no(5,ic) do 312 ie=1,2 do 312 k=ktopkbot,-l is=ktop+l-k if(is.le.nom(l))cvlm=cvol(lic) if(is.gt.nom(l).andis.le.nom(2))cvlm=cvol(2,ic) if(is.gt.nom(2).and.is.le.nom(3))cvlm=cvol(3,ic) if(is.gt.nom(3).and.is.le.nom(4))cvlm=cvol(4,ic) if(is.gt.nom(4).and.is.le.nom(5))cvlm=cvol(5,ic) trf(l,,i,jk,ie)=trf(l,i,jkie)+fldat(l,ie,is,ic)*cvlm voltr(ijk,ie)=voltr(ijk,ie)+cvlm x 312 trf(2,,i,jk,ie)=trf(2,i,jk,ie)+(fldat(lie,is,ic)*cvlm* fldat(2,ieisic))**2 continue c c end tlistal c 313 continue c c Continue for trr data from tlista3 c do 412 loop=1,846 read(18,'(i6,i6,4i3,i6)1,end=433)isqn,ncl,i,jktopkbot,idm2 nom2(1)=no2(lic) nom2(2)=no2(lic)+no2(2,ic) ic=isqn nom2(3)=no2(l,ic)+no2(2,ic)+no2(3,ic) nom2(4)=no2(l,ic)+no2(2,ic)+no2(3,ic)+no2(4,ic) nom2(5)=no2(l,ic)+no2(2,ic)+no2(3,ic)+no2(4,ic)+no2(5,ic) do 412 ie=1,2 do 412 k=ktopkbot,-l is=ktop+l-k if(is.le.nom2(l))cvlm=cvol2(l,ic) if(is.gt.nom2(l).and.is.le.nom2(2))cvlm=cvol2(2,ic) if(is.gt.nom2(2).and.is.le.nom2(3))cvlm=cvol2(3,ic) if(is.gt.nom2(3).and.is.le.nom2(4))cvlm=cvol2(4,ic) if(is.gt.nom2(4).and.is.le.nom2(5))cvlm=cvol2(5,ic) do 412 im=1,5 trr(l,i,jk,ie,im)=trr(l,i,jk,ie,im)+rrdat(l,ie,imisic)*cvlm trr(2,i,jk,ieim)=trr(2,i,jk,ie,im)+(rrdat(l,ie,im,is,ic)* 412 x continue cvlm*rrdat(2,ieimisic))**2 c c end tlistal c 433 continue c do 882 j=1,20 read(15,881,end=882)(itri(i,i),i=1,40) 881 882 format(4Oi4) continue c c c Final processing to get volume averaged flux and cross sections also diffusion coefficient c do 911 j=1,20 do 911 i=1,40 if(itri(ij).ne.O)then do 912 k=1,12 do 912 ie=1,3 c if the flux is not zero, process cross sections if(trf(lijkie) ne. 0.0)then 102 flx(ijk,ie)=trf(l,i,jk,ie)/voltr(i,jk,ie) totxs(ijk,ie)=trr(l,ijk,ie,2)/trf(l,i,jk,ie) absxs(ijk,ie)=trr(l,ijk,iel)/trf(l,i,jk,ie) elsct(ijk,ie)=trr(l,ijkie,3)/trf(l,ijk,ie) diffc(i,jk,ie)=l/(3*totxs(ijk,ie)) fisnu(ijk,ie)=trr(l,i,jk,ie,4)/trf(l,i,jk,ie) fisxs(I.,jk,ie)=trr(l,ijk,ie,5)/trf(l,i,jk,ie) stflx(ijk,ie)=(sqrt(trf(2,i,jk,ie)))/trf(l,ijk,ie) c sttxs(ijk,ie)=sqrt(trr(2,i,jk,ie,2)/ • trr(l,i,jk,ie,2)**2+trf(2,i,jk,ie)/trf(l,i,jk,ie)**2) staxs(ijk,ie)=sqrt(trr(2,i,jk,iel)/ • trr(l,ijk,iel)**2+trf(2,ijk,ie)/trf(l,ijk,ie)**2) • if(fisnu(ijkie).ne.0.0)then stfnu(ijk,ie)=sqrt(trr(2,i,jk,ie,4)/ trr(l,i,jk,ie,4)**2+trf(2,i,jk,ie)/trf(l,i,jk,ie)**2) stfxs(ijk,ie)=sqrt(trr(2,i,jk,ie,5)/ • trr(l,ijk,ie,5)**2+trf(2,ijk,ie)/trf(l,i,jk,ie)**2) endif endif 912 continue 911 continue endif c c Write the results to the file hxl.out c write(11,466) 466 format(/,,Note: gp#1 = fast gp and, gp#2 thermal gp.,,/) write(11,461) 461 formatP • • I J K -,9x,-FLUX TT.XSECTION stdev stdevl,2x,'DIFF.COEFF. ABS.XSECTION stdevllx, NU*FISS.XSECstdevl,2x,'FISS.XSECT stdev') do 894 j=1,20 do 894 i=1,40 if(itri(ij).ne.O)then do 896 k=1,12 kplus=k+4 write(11,462)ijkplus 896 894 • totxs(ijk,2),sttxs(ijk,2),absxs(i,jk,2),staxs(i,jk,2), write(11,463)flx(ijk,2),stflx(i,jk,2),diffc(i,jk,2), fisnu(i,jk,2),stfnu(i,jk,2),fisxs(i,jk,2),stfxs(i,jk,2) write(11,464)flx(ijk,l),stflx(ijk,l),diffc(i,jk,l)I x x totxs(i,jk,l),sttxs(i,jk,l),absxs(i,jk,l),staxs(i,jk,l), x fisnu(ijk,l),stfnu(i,jk,l),fisxs(i,jk,l),stfxs(i,jk,l) continue endif continue c 462 format(3i4,1 g#.) 463 format(14x 1 464 format(14x 2 ',lpel3.5,Opf6.3,lpel3.5,4(lpel3.5,Opf6.3)) stop lpel3.5,Opf6.3,lpel3.5,4(lpel3.5,Opf6.3)) end Program : prohx2n.f program prohx2n c This program processes mctal file of input file outhx2 character*8 kodver character*19 probid character*79title character*4ntalvals character*5 tallykcode 103 c character*2 fdusmcet character*3 tfc character*75 c fcomment integer tallyn(56),pbnameptypenff(90) dimensionxkeff(3),ebin(3),jtf(8) c dimension celln(10000),fldat(2,3,12,5000),rrdat(2,3,5,12,5000) dimension trf(2,60,30,4,3),trr(2,60,30,4,3,3) dimension itri(40,20),itribig(60,30) dimension cvol(5,2166),no(2),nom(2) dimension voltr(60,30,4,3) dimension flx(60,30,4,3),totxs(60,30,4,3),absxs(60,30,4,3) dimensionelsct(60,30,4,3),diffc(60,30,4,3) c real*8 stflxsttxsstaxsstels dimensionstflx(40,20,12,3),sttxs(40,20,12,3),staxs(40,20,12,3) dimension stels(40,20,12,3) c open(unit=llfile=lhx2n.oul,form=lformattedl,status=lunknown') open(unit=13,file=lmclOtlform=lformattedl,status=loldl) open(unit=14,file=ltccl.c2l,form=lformatted',status=lunknown') open(unit=15,file=ltri6OO.2',form='formatted',status=loldl) open(unit=16,file=lvvva.c2l,form=lformatted',status=lold') c • Sequential reading from mctal file, first fluxes then reaction rates • After data has been read subroutines process the data and add it to the • triangle totals of fluxes or reaction rates. write(11,10) 10 format(///5x,'PROHX2.F - AN MCNP TALLY PROCESSING PROGRAM',//) c c Reading the general info about tallies c (not to be processed) read(13,501)kod,ver,probid,knod,nps,rnr 501 format(2a8,al9,i5,illil5) write(11,5011)kod,ver,probid,knod,nps,rnr 5011 format(ITally file:,/,ImclOtl,2x,2a8,al9,i5,illil5) c read(13,502)title 502 format(lxa79) write(11,502)title c c nt=56 read(13,503)ntalnt 503 format(aSi5) 600 format(16i5) c read(13,600)(tallyn(i),i=1,nt) c c ***** Start tally loop c nfkeepl=l nfkeep2=0 nfkeep3=1 nfkeep4=0 do 100 n=lnt read(13,504)tallypbnameptype 504 format(a5,M) read(13,505)fcomment 505 506 format(5xa75) read(13,506)fnff(n) format(a2,A) nf=nff(n) if(n.le.18)then 104 nfkeepl=nfkeep2+1 nfkeep2=nfkeep2+nf endif if(n.gt.18)then nfkeep3=nfkeep4+1 nfkeep4=nfkeep4+nf endif if(n.le.18)read(13,507) (ce11n(i),i=nfkeep1,nfkeep2) ifi:n.gt.1S)read(13,507) (celln(i),i=nfkeep3,nfkeep4) 507 format(110) read(13,506)didumm read(13,506)uidumm read(13,506)sns if(ns.eq.O)ns=l read(13,506)mnm if(nm.eq.O)nm=l read(13,506)cnc if(nc.eq.O)nc=l read(13,506)ene read(13,509)(ebin(i),i=1,ne-1) 509 format(lp6e13.5) read(13,506)tidumm read(13,510)vals 510 format(a4) c Readlist of tally/error c data pairs if(n.le.18)then read(13,511)((((fldat(it,ie,is,ic),it=1,2), 511 x ie=1,3),is=lns),ic=nfkeepl,nfkeep2) format(4(1pe13.5,Opf7.4)) endif if(n.gt.18)then read(13,511)(((((rrdat(it,ie,im,is,ic),it=1,2), x ie=1,3),im=lnm),is=lns),ic=nfkeep3,nfkeep4) endif c c Read tally c fluctuation data read(13,512)tfc,nfc,(jtf(i),i=1,8) 512 format(a3,i5,8i8) do 150 j=lnfc read(13,513)npsxtallyxerrfom 513 150 format(illlp3el3.5) continue c c ***** End of tally 100 continue loop c c Read kcode data c read(13,3000,end=999)kcode,ncycle 3000 format(a5,i5) do 200 ncy=1,ncycle read(13,3010,end=999)(xkeff(k),k=1,3),dummyl,dummy2 200 continue 3010 format(lp5el2.5) 999 continue c c Read segment volume data from vvva.c2 c x do 413 ic=1,1210 if((ic.le.36).or.(ic.gt.78.and.ic.le.300).or. (ic.gt.540.and.ic.le.570).or. 105 x (ic.gt.642.and.ic.le.846).or. x (ic.gt.846.and.ic-le-1102))then read(16,*,end=417)ic,cvol(l,ic),cvol(2,ic) endif if((ic.gt.36.and.ic.le.78).or. x x x (ic.gt.300.and.ic.le.462).or. (ic.gt.570.and.ic.le.642).or. (ic.gt.462.and.ic-le-540).or.(ic.gt.1102))then read(16,*,end=417)iccvol(lic) endif 413 continue 417 continue c c Read the rest of the conversion data for flux from tccl.c c do 312 loop=1,1210 if((loop.le.36).or.(loop.gt.78.and.loop.le.300).or. x x (loop.gt.540.and.loop.le.570).or. (loop.gt.642.and.loop.le.846))then no(1)=1 no(2)=l ktop=4 kbot=3 endif if(loop.gt.36.and.loop.le.78)then no(1)=1 ktop=4 kbot=4 endif if((loop.gt.300.and.loop.le.462).or. x (loop.gt.570.and.loop.le.642))then no(1)=1 ktop=3 kbot=3 endif if((loop.gt.462.and.loop.le.540).or.(loop.gt.1102))then no(l)=4 ktop=4 kbot=1 endif if(loop.gt.846.and.loop.le.1102)then no(1)=1 no(2)=2 ktop=3 kbot=l endif nom(l)=no(l) nom(2)=no(l)+no(2) read(14,'(i6,i6,2i3)',end=313)isqn,ncl,ij ic=isqn do 312 ie=1,2 do 312 k=ktopkbot,-l is=ktop+l-k if(is.le.nom(l))cvlm=cvol(lic) if(is.gt.nom(l).and.is.le.nom(2))cvlm=cvol(2,ic) x trf(l,ijk,ie)=trf(l,i,jk,ie)+fldat(l,ie,is,ic)*cvlm voltr(i,jk,ie)=voltr(ijk,ie)+cvlm trf(2,ijk,ie)=trf(2,ijk,ie)+(fldat(l,ie,is,ic)*cvlm* fldat(2,ieisic))**2 if(ic.eq.918)then trf(1,19,8,k,ie)=trf(1,19,8,k,ie)+fldat(l,ie,is,ic)*cvlm vo.itr(19,8,k,ie)=voltr(19,8,k,ie),+cvlm trE(2,19,8,k,ie)=trf(2,19,8,k,ie)+(fldat(l,ie,is,ic)*cvlm* fldat(2,ieisic))**2 106 x endif do 312 im=1,3 trr(l,i,jk,ie,im)=trr(l,ijk,ie,im)+ x rrdat(lieimisic)*cvlm trr(2,i,jk,ie,im)=trr(2,i,jk,ie,im)+(rrdat(l,ie,imis,ic)* cvlm* rrdat(2,ieimisic))**2 x if(ic.eq.918)then trr(1,19,8,k,ie,im)i=trr(1,19,8,k,ie,im)+ x rrdat(lieimisic)*cvlm trr(2,19,8,k,ie,im)=trr(2,19,8,k,ie,im)+(rrdat(l,ieim,is,ic)* endif 312 x cvlm* rrdat(2,ieimisic))**2 continue c c end tccl.c c 313 continue c c c read triangle mesh from tri6OO.2 c do 882 j=1,20 read(15,881,end=882)(itri(i,j),i=1,40) 881 882 format(4M) continue do 885 j=21,30 read(15,886,end=885)(itribig(i,j)li=41,60 886 format(2M) 885 continue c • Final processing to get volume averaged flux and cross sections • also diffusion coefficient c do 911 j=1,20 do 911 i=1,40 if(itri(ij).ne.O)then do 912 k=1,4 do 912 ie=1,3 c if the flux is zero set xsections to zero automatically if(trf(lijkie) ne. 0.0)then flx(ijk,ie)=trf(l,i,jk,ie)/voltr(i,jk,ie) totxs(ijk,ie)=trr(l,ijk,ie,2)/trf(l,ijk,ie) absxs(i,jk,ie)=trr(l,i,jk,iel)/trf(l,i,jk,ie) elsct(ijk,ie)=trr(l,ijkie,3)/trf(l,ijk,ie) if(totxs(ijkie).ne. 0.)diffc(i,jk,ie)=l/(3*totxs(ijk,ie)) c stflx(i,jk,ie)=(sqrt(trf(2,i,jk,ie))-)/trf(l,ijk,ie) sttxs(i,jk,ie)=sqrt(trr(2,i,jk,ie,2)/ • trr(l,i,jk,ie,2)**2+trf(2,i,jk,ie)/trf(l,i,jk,ie)**2) staxs(ijk,ie)=sqrt(trr(2,i,jk,iel)/ • trr(,li,jk,iel)**2+trf(2,i,jk,ie)/trf(l,i,jk,ie)**2) endif 912 continue 911 continue endif c c Write the results to the file hx2.ou c write(11,466) 466 formatU,'Note: gp#l = fast gp and, gp#2 thermal gp.',/) write(11,461) 461 format(' x I i K 1,9x,'FLUX TT.XSECTION stdev stdevl,2x,'DIFF.COEFF. ABS.XSECTION stdevl) 107 , do 894 j=1,20 do 894 i=l 40 if(itri(ij).ne.O)then do 896 k=1,4 write(11,462)iik write(11,463)flx(ijk,2),stflx(ijk,2),diffc(ijk,2), write11,464)flx(ijk,;),stflx(i,jk,l),diffc(i,jk,l), • totxs(ijk,2),sttxs(ijk,2),absxs(i,jk,2),staxs(i,jk,2) • totxs(i,j;k,l),sttxs(i,jk,l),absxs(i,jk,l),staxs(i,jk,l) 896 continue endif 894 continue c c graphite reflector c do 941 j=21,30 do 941 i=41,60 if(itribig(ij).ne.O)then do 942 k=1,4 do 942 ie=1,3 c if the flux is zero set xsections to zero automatically if(trf(lijkie) .ne. 0.0)then flx(ijk,ie)=trf(l,ijk,ie)/voltr(ijk,ie) totxs(ijk,ie)=trr(l,ijk.,ie,2)/trf(l,i,jk,ie) absxs(i,jk,ie)=trr(l,i,jk,iel)/trf(l,i,jk,ie) elsct(ijk,ie)=trr(l,ijkie,3)/trf(l,ijk,ie) if(totxs(ijkie).ne. 0.)diffc(i,jk,ie)=l/(3*totxs(ijk,ie)) c stflx(ijk,ie)=(sqrt(trf-(2,i,jk,ie)))/trf(l,ijk,ie) sttxs(ijk,ie)=sqrt(trr(2,i,jk,ie,2)/ • trr(l,i,jk,ie,2)**2+trf(2,ijk,ie)/trf(l,ijk,ie)**2) staxs(ijk,ie)=sqrt(trr(2,i,jk,iel)/ • trr(l,ijk,iel)**2+trf(2,ijk,ie)/trf(l,ijk,ie)**2) endif 942 continue 941 continue c c endif Write the results to the file hx2.ou c do 994 j=21,30 do 994 i=41,60 if(itribig(ii).ne.O)then do 996 k=1,4 imin=i-40 jmin=j-20 write(11,465)iminjmink write(11,463)flx(ijk,2),stflx(ijk,2),diffc(i,jk,2)I write(11,464)flx(ijk,l),stflx(i,jk,l),diffc(i,jk,l), • totxs(i,jk,2),sttxs(i,jk,2),absxs(i,jk,2),staxs(i,jk,2) • totxs(i,jk,l),sttxs(i,jk,l),absxs(i,jk,l),staxs(i,jk,l) 996 continue endif 994 continue 462 463 464 format(3i4,1 format(14x format(14x gp#') 1 pel3.5,Opf6.3,lpel3.5,2(lpel3.5,Opf6.3)) 2 lpel3.5,Opf6.3,lpel3.5,2(lpel3.5,Opf6.3)) 465 format B- c c 3 (i3, gp#') stop end 108 Program : sibell character*6titl character*1 + + adum integer cnumvnum dimension cnum(3,1000),flx(3,2,12,1000),abx(3,2,12,1000), tox(3,2,12,1000),elx(3,2,12,1000),fnu(3,2,12,1000), fis(3,2,12,1000),vnum(200),vol(200),indt(3,1000) dimension tabx(12,2),ttx(12,2),telx(12,2),tfnu(12,2), + c c c c 3 2 12 100 tfis(12,2),tf1x(12,2) nf 1=8, 2=9, 3=10 ie is cell number ifile open(unit=Bfile=lmcn2.inpl,form=lformatted',status='old') open(unit=9,file=lmcn5.inp',form=lformattedl,status=loldl) open(unit=10,file=lmcn4.inpl,form='formatted',status=lold') open(unit=llfile=lvol.outlform='formattedl,status=lold1) open(unit=12,file=lrsltslform=lformattedl,status=lunknown') c do 8 nf=1,3 ifile=nf+7 icn=O 10 read(ifile,,(a6,i6,/)',end=88)titl,numl if(titl.eq.lltallyl)then if(numl.eq.124.or.numl.eq.334.or.numl.eq.214)itype=1 if(numl.eq.134.or.numl.eq.344.or.numl.eq.224)itype=1 if(numl.eq.144.or.numl.eq.354.or.numl.eq.234)itype=1 if(numl.eq.164.or.numl.eq.364.or.numl.eq.244)itype=2 if(numl.eq.174.or.numl.eq.374.or.numl.eq.254)itype=3 if(numl.eq.184.or.numl.eq.384.or.numl.eq.264)itype=3 if(numl.eq.194)itype=l if(numl.eq.204)itype=3 elseif(titl.eq., cell )then icn=icn+l cnum(nficn)=numl indt(nficn)=itype if(itype.eq.l)then read(ifileI(a)I)adum do is=1,12 read(ifile,*)idum,flx(nflis,icn),rdum,flx(nf,2,is,icn) c c + write(12,1(3h #0,2i7,1p2e13.5)1)cnum(nficn), enddo icn,flx(nflis,icn),flx(nf,2,is,icn) read(ifile,'WI)adum if(itype.eq.2)then read(ifileI(a,/)I)adum endif do is=1,12 read(ifile,*)idum,fnu(nflis,icn),rdum,fis(nflis,icn), rdum,abx(nflis,icn),rdum,tox(nflis,icn), + + rdumelx(nf,1,isicn),rdum enddo read(ifi1eI(a,////)I)adum do is=1,12 read(ifile,*)idum,fnu(nf,2,is,icn),rdum,fis(nf,2,is,icn), rdum,abx(nf,2,is,icn),rdum,tox(nf,2,is,icn), rdumelx(nf,2,isicn),rdum + + enddo read(ifile,,(a,/////////////////)')adum endif if(itype.eq.3)then read(ifileI(a,/)')adum read(ifile,*)idum,abx(nflis,icn),rdum,tox(nflis,icn), do is=1,12 109 + rdumelx(nflisicn),rdum read(ifile,,(a,////)')adum enddo do is=1,12 read(ifile,*)idum,abx(nf,2,is,icn),rdum,tox(nf,2,is,icn), rdumelx(nf,2,isicn),rdum + enddo endif c read(ifile,'(a,/////////////////)Iend=88)adum write(12,*)nficncnum(nficn) endif goto 88 0 continue do i=.1,193 read(ll,*)idumvnum(i),vl vol(i)=vl/12. c write(12,*)idumvnum(i),vol(i) end do do 90 =,193 tvol=tvol+vol(i) if(i.le.37)then nconv=vnum(i)-71000 nf=l elseif(i.gt.37.and.i.le.113)then nconv=vnum(i)-11000 nf=2 elseif(i.gt.113)then nconv=vnum(i)-81000 nf=3 endif do 90 j=1,1000 if(nf.eq.l)ncmp=cnum(nfi)-81000 if(nf.eq.2)ncmp=cnum(nfj)-42000 if(nf.eq.3)ncmp=cnum(nfi)-82000 if(ncmp.eq.nconv)then write(12,*)i,vnum(i),cnum(nf,i),nconvncmp,nf do is=1,12 do ie=1,2 if(indt(nfi).eq.l)then tflx(is,ie)=tflx(is,ie)+flx(nf,ie,isj)*vol(i) endif if(indt(nfj).eq.2)then tfnu(is,ie)=tfnu(is,ie)+fnu(nf,ie,isj)*vol(i) tfis(is,ie)=tfis(is,ie)+fis(nfie,isj)*vol(i) tabx(is,ie)=tabx(is,ie)+abx(nf,ie,isj)*vol(i) ttox(is,ie)=ttox(is,ie)+tox(nfie,isj)*vol(i) telx(is,ie)=telx(is,ie)+elx(nf,ie,isj)*vol(i) endif if(indt(nfj).eq.3)then tabx(is,ie)=tabx(is,ie)+abx(nf,ie,isj)*vol(i) ttox(is,ie)=ttox(is,ie)+tox(nfie,isj)*vol(i) telx(is,ie)=telx(is,ie)+elx(nf,ie,isj)*vol(i) endif enddo enddo endif 90 19 continue write(12,19) format(' x K gp#1,5x,'FLUX',4x,'TOT.XSECTIONI,2x, 'ABS.XSECTION',lx,'NU*FISS.XSECI,2x,'FISS.XSECTI) nn=O do 91 is=12,1,-l nn=nn+l do 91 ie=2,1,-l if(ie.eq.2)iee=l 110 if(ie-eq.l)iee=2 flux=tflx(isie)/tvol siga=tabx(isie)/tflx(isie) sigt=ttox(isie)/tflx(isie) sige=telx(isie)/tflx(isie) sigf=tfis(isie)/tf1x(isie) sfnu=tfnu(isie)/tflx(isie) write(12,20)nn,iee,flux,sigt,siga,sfnu,sigf 20 format(2i3,lp5el3.5) 91 continue write(12,*)nniee,fluxsigt,siga,sfnu,sigf c write(12,1(13h stop total vol = lp5el3.5)1.)tvol*12 end File : rsits K 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 total gp# 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 FLUX 3.64298E-04 7.13615E-05 4.47630E-04 6.83401E-05 5.13602E-04 7.25782E-05 5.45928E-04 7.66283E-05 5.36221E-04 7.25827E-05 5.04040E-04 5.97613E-05 4.49893E-04 4.91919E-05 3.92346E-04 4.20241E-05 3.41173E-04 3.55777E-05 2.81711E-04 2.96850E-05 2.32209E-04 2.47867E-05 1.69892E-04 2.40555E-05 vol = TOTASECTION ABS.XSECTION NU*FISS.XSEC 5.54066E-01 2.29585E-03 1.87641E+00 3.3620SE-02 5.62481E-01 2.28250E-03 1.81449E+00 3.16205E-02 5.64775E-01 2.23828E-03 1.78767E+00 3.141OOE-02 5.70975E-01 2.32829E-03 1.79394E+00 3.16111E-02 5.69695E-01 2.25072E-03 1.78241E+00 3.18629E-02 5.77033E-01 2.26380E-03 1.74026E+00 3.17982E-02 5.78575E-01 2.32567E-03 1.72769E+00 3.18037E-02 5.80923E-01 2.39860E-03 1.71519E+00 3.19280E-02 5.78941E-01 2.47606E-03 1.69937E+00 3.17879E-02 5.79020E-01 2.47141E-03 1.70773E+00 3.20984E-02 5.79536E-01 2.43172E-03 1.74561E+00 3.35301E-02 5.75283E-01 2.38011E-03 1.77757E+00 3.56112E-02 2.97691E+03 ill 9.05881E-03 2.85794E-01 9.16390E-03 2.66815E-01 9.00610E-03 2.65587E-01 9.42292E-03 2.68949E-01 9.20519E-03 2.75376E-01 9.28217E-03 2.80191E-01 9.42908E-03 2.85593E-01 9.52839E-03' 2.87597E-01 9.80863E-03 2.87257E-01 9.63444E-03 2.93157E-01 9.80162E-03 3.06559E-01 9.59636E-03 3.31846E-01 FISS.XSECT 3.68822E-03 1.1728BE-01 3.73346E-03 1.0949BE-01 3.66894E-03 1.08994E-01 3.84006E-03 1.10374E-01 3.7512BE-03 1.13012E-01 3.78327E-03 1.1498BE-01 3.84369E-03 1.17205E-01 3.88470E-03 1.18027E-01 3.99929E-03 1.17888E-01 3.92791E-03 1.20309E-01 3.99709E-03 1.25809E-01 3.91062E-03 1.36187E-01 APPENDIX C SAMPLE CROSS SECTION RESULTS 'Me sWisticals effors are given as ftwtions of the mean values (not percent). 112 OD -4 C 14 x(1) C En H r- E- U w (n x a 0 : 1 1 C) 0 CD 0 () C) I -4 C) I (In 1-4 0 C) I I d. 'A I'm 1-4 r-4 Ln C,) ON (1) ON Iq Cq C14 al 1-4 CD (14 'O -4 r-1 OD 1 C C 1 C! 1 1 1 1 1 C! 1 C) 0 C C C > C C C) 0 C) C) (n C) -4 0 C,) -4 C) 0 10 C) CN 0 (n C) 1-4 0 () a 1-4 rn -4 C) C) 11) 1-4 C) CD () -4 C) a 1 114 ;:r ON r14 1 0 ol WI C 1-4 10 'IC q Id, m Ln (1) U') Ln C) 10 a) W r%D OD I'd, r0 0 o r10 C) r- Ln CD m Lf) C) 00 -4 1-4 OD li C L r ODrUl Ln C C 01) clq OD CN I 1-4 a CN r4 14 w w L r- CN OD co C4 U.) m clq 10 CN Ln CD oll C,) 1-4 0 C C),%1.0 1-4 v 00 m Ln -* CD m 10 1-4 OD CT rq ) r- C) LI) 0 CN Ch 'IO ,-;r Lf) ON 11 0) (n CN CD CYN(14 Ln r- Lr) -4 Ln -4 W W Ln Clq 14 1 C C C C ( C) C) C C CD (n -4 C) C) cn 0 -4 0 C,) 1-4 0 C) r 0 14 clq W 14 00 1-4 W W 10 -4 CN I'm 00 Li k9 ko -o I'm C CN o -4 C r- Cn CN C C14 1-4 C) L co -4 o a) " OD 00 ko ( CN r N CN 'A I'D 1-1 1-4 a% -i -4 -4 ON -4 -4 1-4 a% -i -4 A 'IO r- -o C) LI) C14 1-4 CN 1-4 r- (1) Lc N C14 --I w 'A -4 -4 'IO 1-1 -4 1-4 ( C C! C (: C CD ( 0 C C) ( C (: C ( C C C CD ( C CD CD 1 C) C 0 C C C! C C C 1 C C C C> C C C ( C (: (: CD ) cn 0 CN C) M 0 CN 0 rn CN C) C) M 0 CT 0 (1) C14 C) CD -:r C14 Cq cn C13 fn C14 m M C14 C,) 04 -4 0 C) co (n OD Ln 1-4 C14 Ln C14 C,) r- r- Ln LI) 1.0 r- C,) 0 C,) a:) ID C) C) r- '4 m -r -4 0 Ir Ln CT 'IO 'IF D C) OD Ln U-) U-) m Ln Lr! 1! I a li C r ( (: -! ( 1-4 -4 C14 -4 C14 L -4 " 14 -4 CN 1 C ! C ( C -4 1-4 1-4 1-4 (11 clq 0 0 1) C13 C) 0 114 OD -1 ll-r 00 1-4 0 r-4 C14 OD 10 'IO 14 00 OD CN 10 M C14 m 1-4 kD r, 0 m aD Ln r- C) co 00 Ln C> co o Lf) C14 a) ko OD co co -4 10 C> -4 -4 1 ( C9 : " 1 1) C CN (1) C "! Clq M li " C m C " r m L -4 Ci C13 1 D CN -4 ko 0 (14 14 D CN Li C) CN -4 D C) C) WI 1-1 m k.0 r 14 C 1-1 I'm Ln 1-4 C) 1-1 kD C14 C> C!( 1 1 C) CD ( ( C) C) ( C) C) C) C) -4 C) -4 C) C) -4 0 C) C) C) CD C) 4 0 C C) 0 C) 14 1.0 r- " C) IC o CN 10 4) 1 1 C> C) C) 2 Ln (7, rLn r C> m 'D 'n .0 rCN 4 a r- OD (=, OD C, rko c Ul -4 kD 10 C) 1-1 1.0 CN C) -4 .o CN C:) -4 LO 1-4 C) 14 0 C) 9 9 0 0 9 9 C) C) 9 9 9 9 C) C) -4 C) 0 0 1-4 C) 0 C) --I -- I 0 0 1-4 C) C) 0 1-4 C) 0 C) -4 0 C) 0 -4 C) C) 0 1-4 C) 0 0 -i C) C) CD WI CN C14 W+ C) 1-4 WI W+ (n 114 r+4 m -4 C) WIW+ I'D 0 a 1.0 I0 ko 'o rU.) c 0 -4 a, '.0 C> CD a W+ a () c:) M c C) -4 0 co CN ( c C) q m 00 -0 1-1 1-1 1-4 1-4 -4 -4 -4 1-4 1-4 -4 1-4 -4 -4 -4 1-4 -4 1-4 0 a a C) C) 0 CD C> C) 0 14 14' r4' W W 14 W W -4 (n 1-4 C) OD 10 1.0 ko C) U) ko m ko LO 10 (1) I" 10 ac) o Ln r- a clq m 10 14 IV U') r- 'IO ko 1-4 r- C 1 1 (, I r ( r .=! r LO U) %.O 1-4 Ln -4 W -4 -4 rm M -4 -4 -4 Ln CY% OD rC> 0 ko r- -4 r- C) r- q rco ra -0 rlco m 9 9 1-4 co 14 m r0 Ul 1-4 -4 CN a) 9 9 -4 -4 m 14 C,) OD kD C) 14 Le) C4' 1 co C14 ( 9 Iq CD C) r- C) C) 0 m 1-1 -4 Ul r4' r4' 10 1-4 0 0 14 1-4 q CD C) C) m C14 0 C) C!C LO r4' C) 0 ( 9 1--i 4 r- WI r+4 14 OD 114 r+4 r- 0) .0 co 1-4 -4 C) C) Ln q. Lc) m 0 10 1-1 it W+ Cq %D C,) CD 'o " -4 CD CD --I 0Ln r- r+ co r- o d. I-W 14 r- 0 19 19 -i rl) 14 Lr) -4 rn CN C14 'A 0 1 4 1 : C) Ln E L I-zr -4 : r.: 1-4 1-1 C)0 014 14I 14I w 0 llp 4 C ") m 0c) m C13 C.. 04 -V 1-4 1 C W+ -4 co 0 -W --I C CD C) E- Ln 1-1 C) C) 'iE- Ln -4 1 'IO EW co In 1-4 C) W z 0 H r--I 1 c R C) CN --I C) -4 a Clq0 cl cn C) 00 1-4 r ll r k 1 C14 OD ko m C) C14 E+4 m r- WI r+ WIW+ -4 1-4 'IO 10 C) 'o (,4 rm C) ,q C, co C13 ") (7% .0 o r 1-4 r, 'r 00 L, r Ln -4 -0 -4 Lf) 1-1 U-) -1 Lf) q -4 -1 C> C) -4 a 'A C) -4 0 -4 0 1-4 0 _q 0 ] 14 14' r4' 14 C4' r4' r4' C) -4 CIA C) L 'IO r CN 1-4 0 a, c,4 LO 'IO -4 OD co kD -) 10 0) 0 00 ON 'IT CN 1.0 CN %OCN %D I-f 110 14 Ln kD 'IO -0 O r M ko C) r- C14 -4 'IO t) m L,) 1-1 co c CD C) 0 0 to r1 ( r- 110 fn Ln r co ao C) 10 I=! C (1 r (1) r- (1) r- (n rC) C C,) r- 10 C) r- Clq Ln -4 0 14 1-0 0 10 C) C) -4 10 rC) C) m rC C rl) ID C) CD 1 0 1 CD (: C) = C C 0 ( C) = C) ( ( C) ( C 0 ( C) ( 0 1 C> ( 0 C C) ( C) 1 1 0 1 C) C C) 1 C C .,:! 0 ( C 1 CD 10 Ln -0 a I w Ln " Ln -o 10 -0 0 Ln C) 10 C> Ln a .0 C) Ln C> 10 Lf) -0 Ln -M U) I-V Ul 10 Ln C) Ln C) -D 10 (D C) C) a 0 WI 04 C r4' 1 WI C C OD aN C4 10 1-4 1-4 a) oll 1.0 OD 00 CT C> clq L.n 00 1-4 1-4 m (1) Ln Ln Ln OD U) 10 Ln 1 C4 OD ID a% C,) OD 1-4 cli Ln 00 (, M (: r- I ( (, L -4 CN 1-4 CN -4 CN C> C C> CD CD CD C> C> C> -4 C> -4 C> -4 ) 4.) -r Ln CI C) 11 C14 ft a W W r 4 tm 'j Ln a00rnm x r. D 11 (v f-4 (1) Ln 1 C r- zo -, CN" C) C) I 1 w r- rr- (n Ln Ln (1) en C (1) r1.0 1 10 ON1-4 ODlZ "I 0 WI w clq ko U) 10 0 ON clq Cq " :w 10 I r kV (1) rr- Ln a 0 U) 0 0 ko r I :0 m r- 40 un -4 10 14 Ln a) %D (1) k9 m Ir- O I C,) r- :0 (1) OD O 1 :0 C> C) I CD CD I CD CD I r- 'IO 1-4 C> 10 OD C C) -4 C In 'IO CN C> Ln kD 1.0 Ln OD 10 C14 kD C> L C 1 r -4 cq 1-4 CN C) 10 rn r- 1-4 0 Ul m 00 00 0 m r 10 1.0 Z* 9 4i U) (O 4 I a t3l tm -4 'N a-4 U) C-4 a -I tm C4 011-1 tm cq " tR 1-4 C'4 a tm -4 CN a ty) 4 CN O. m w :w U) :* 1-4 CT m Ln r- OD ft t3) ZW 14 C14 tm tm m 0 14 1-4 1-1 clq -4 m 1-4 1-1 1-4 1-4 -4 -4 1-4 cq CN clq m m U) ko r- CN m 11 1-4 t3l 4i " 1-4 -4 -4 14 1-4 1-4 'A -4 -4 (N m LI) 1-4 1-4 -4 1-1 CN CN C14 m 112 -4 'r m (-) -1 CT ,: ( r1l co rl) 1.0 CN10 r- I'D (n -4 -1 1-4 (1) 1-4 -1 r- r- -1 -I -4 C) r- m r- m Irp m 10 .o a C14 1 -4 -4 1-4 -4 - CN Lf) (1 l -1 -4 -4 q (14 Ul 11 : ( : : 1 C : 9 9 9. 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 C: 0 CD CZ) C C CD CD C C C C C a CD C C C C C C) C> C) CD CD CD CD (1) -4 I-zr CN In 1-4 (n M 1-4 ff) 1-4 ff) 1-4 m -4 M -4 rl) 1-4 a -4 m -4 m -1 O W W 1 r Lc) LO C) I-Im 10 r- ff) 1-4 1-4 T C) -4 C) 0 1-4 Le)10 C14 rl) (1) 'IO 'IOON r C rr- m lmr1-1 CZ)ID rr- m m Ln c) ac) C C4 a:) a% m 1-4 U,) 0 ID a) I'D ID OD CN r- C C : ,-* 'IO OD L (13 L OD C14 1-4 co -4 1-4 1-4 C W 00 10 co (1) l W 1-tvCN co 10 0) -4 19 o CN 0 C ff U Clq Ul ( O 19 C14 r- -1 1-1 C14 eq Iq (1) CN CN 1-4 Ch CN CN 1-4 CN r- CN r- 'IO 14 co ON aD (,) -4 -1 r-4 C? m 1-1 m rn 'IO co r1-4 00 0( Ul O 1 O 1-99 CN 00 ID Clq C r- -4 1-4 OD -4 1-4 1-4 1-4 rl) CN 14 1-1 () cq 14 CN(n 1-4 1-4 OD0 cq C? 0 C) > C) C) CIq (1) ko cq Cl) CN 0) Ln 1 CN 7 00 L (N 00 (14 OD CN r-4 r-4 CN -4 Cl) a 1-4 1-4 0 OD cq rI-zrCD a) r- m r10 1-4 -D U-) r L Ln kD -4 1-4 r-4 ,: ( C( 9 : : 9 9 9 9 9 9 9 9 9 9 9 9 9 ` 9 9 9 1 (: 9 CC C) C) C) CD a C) C) O 0 C) C> C) C) C) O O C) CD C) CD CD (-) C13 C> C) (1) CN CD 0 m (14 C> C) m C) " C) (1) (14 C) C) m C) C13 CD (1) CN C) C) Cl) CN C) CD (1) C) W W .;T CN W W m OD C) C) Ilzv clq C) 0 CD (1) " C) CD CN co k.0 0) LI) r- r(n 1-1 ao 0 (7N Lf) r- " 0) 1-11 m 0 r- ( ( 0 -4 L -4 U) 0 Ln ID r- Lr) 0 CII CD clq m 14 1-4 m -4 -4 cq cq " Cl) -4 Ln 1-4 C) -4 I'D -4 C) -4 ko 0 ID C14 C) 14 o 0 10 1-4 U) -4 C) -4 Ln -4 0 -4 1 O 1 1 C) a 1 0 1 ( C) O C! 1 C) 0 : ( C) C) ( 0 1 C. : ( C) 0 0 0 'A 0 1-4 C) C -4 0 1-4 0 O -- I C) O -1 0 0 0 -1 r4' r+4 10 m L( r- W C+4 W r+4 1-4 rl) ID 'IO (,) a% co 1-4 Cq -4 W W 10 Cq 10 ko r4' W (1) C) a 00 0 1-4 Ln rl) r- -4 Ln -4 (14 Cl) 00 o CD 1-4 C) 0 1-4 CN ko 0 ( 0 ( ( C) 0 1 C) -4 0 -4 0 1--i C> C C + Lf) r- CT -4 CN 1-4 1.0 o 10 ko -A C-) CN c 1-4 0 a a 0 r Lr) co ko LI) W r+4 rI-Ir rCl) r+4 0) LI) CN -IV Ul (n .o OD LI) -4 O r- .o Ln m C> ODOD 10 m -4 OD U,) 1.0 L C C) rn Cq CD CD (D C) r- Lr) 1-4 r- rn CN (1) clq C) C) O oll Clq m r C) co aN (1) m Lf) Ln M Lr) 0 en ( a 0 I-M co --I -4 a ! roll 1-4 r- clq -4 C) 0 rC14 -4 -4 CN 'n OD C) m r- ko co 0 m Lr) 0) Ln 0) " Ul -4 CN Cl) clq CN (N Cl) o CN C) -4 LI) cq O -4 -V 14 C) 1-1 Ln " C) 1-4 0 co 1-1 ( ( C) 0 ( 1 C) 0 1 1 C) O 1 0 C! C) 1 CD -4 0 -4 0 C) 0 1-1 C) D 1-4 0 O ) W CD cq 10 co r14 f+4 -4 -, aN CN -4 C) CD I WI W %D C,4 (1) m 0) r, 'D : -! CN 0 0 1 C+4 1-4 co r- r- -! a Ln ID -! c Cl) 1 C) W r+4 1-4 'D C14 r- W rrl) r- P H Lr) co 0) '.cv Ln w rCq co 'D C,4 cn (n IV 'o C) C) 'o CN Zo . Ci -:r 1-1 . C Ul -4 . C Ul -4 . L Ln q . C VI 1-1 . 1 Ln -4 . C VI 4 . ( Ln -4 co ko r(n 0 O r4 m aN 00 C) CD m c) aN CNr1-1 co ko a) r r m CN CD U., Ul .m OD a, r, LI) U) 1-4 --q 1-4 CD C) 1-4 -1 C) CD -1 -4 C) a -4 -4 C> 0 --I -4 0 C) -4 0 0 1-4 1-4 0 C) -4 14 O C, 1-4 -4 C) 0 1-1 14 0 (D -4 O 1-4 0 --I 1-4 C) C) -4 -4 C) C) 1-4 11 C) O r r4 w Ln Le -4 r- m W W CN 00 C) W r4' Ln rr- 10 (n Ch CN1.0 14' W co C) (1) OD W OD 1-4 a) m W r4' r- CN -4 " -;v r4' W -4 " C) 00 o) aN C) Ln r4' r4' -4 rCl) 'IO m -4 fl) OD OD %-O ( c w o (1) Ln c r oll 0) C14 clq c r 0) -4 r-4 m M Ln C11 0) ON W O 1-4 m w 10 Lr) a% D W -4 10 m .o 1 v 00 r-,r 14' (D -4 rai 14' W U) Ul r- Lr) 10 Ul CNra a 14' DQ k-0 -;r r- 0) a:) rw C) W D 1-4 m r- -4 m 1-4 CD (n w CN co Lr) -4 Ln Ln 1-4 Ln %.OCN r- CN Ln w kD Ln 1-4 Ln 14 1.0 14 U) -4 1-4 -0 -4 0 -4 C) OD Ln clq c r m a m rl) a -4 . 1 Ln -4 W r4' U) C) -4 r- ( m W Ln C) C Ln 1-1 -0 . (, Ln -i c C) ID CN -4 1-4 Ln co 0 0 Ln r9 1 Ln C14 'A r- 1-4 q A 1-4 -4 W m CN ro : o ( c LO 1-4 1.0 C11 ff) OD Cl) r- (1) r- (1) r- 1.4,r0 0 I-zrC) Cl) r- Cl) r- (n OD m r- (14 r- m tC) 0 m aD C) C) 1 1 1 1 1 1 O C) : C C) C) ( 9 ( : ( C ( ( ( 1 1 1 C! 1 1 1 1 1 0 C) : : C) C) C C 10 LI) 10 LI) I'm 10 LI) CD CD C) 0 10 CD U') C) I-M Ln CD C 1-0 C) -V U) CD Ln C) " C) -W C) V- U) C, 10 C) Ln C) C) 0 C) C=> 0 0 1 r4l Ln U-) OD C C4 I'D 1.0 l W r- (ON 4' l CT W l j 0) %.0 l 3 aN CN j W Ln r- W l Ln %D W r4' m Cl) 'IO 0 C14 D rLf) Ln en a Clq m Ln 'IO LI) m 0 10 1-4 ON 00 -4 m -4 C) C:> 1-4 C) 1-1 C) C) CDC) C) C) o U') C) C> 0 I Ln U) kD 1-4 OD kD -4 r- 10 10 1-4 LI) m kD Ul %D I* C> 10 co 10 Ln -0 m OD r- O I r 1 -! ll 111:r r- -v %O cl Ll rn co C) C) C) C> CN C14 1-4 m 10 r) (1) r- 1! (1) a C> Ln C) I co 0 C) C) -W W Ln CN C14 OD () C14 1.0 co i r- I c) C) 1-4 -4 CN 0. U) 1-4 rl) 'A CN at:n r- 1-4 m Ul A Cq 41: aM ao 1-4 Iq CN aU) m 4 cnl rl) r- OD -4 CN a *c M 0 CN -4 -0 C) C> O C) C C) C) C) C) o Ln C) 1.0 LO ko C) C> Ln C> 10 C> ko C> Ln C) O C> C) C) O C) C) en C r- C L ko CN 0 a CD %.D 41t ft a t3l 04 0) CN Cq 04 M 4 Ln 'IO r- C O m 104 -4 --q -4 C) (1) CN 0 CD Ln 'IO00 1-1 C 0 tm -1 C C C ZW a 1-4 M 4 ,, Ln IV . r- U) - (N n Cl) (n C) CN Ln C14 CD Lr) CIA Ull 1-4 1 zw I-zr Ln C) C) I I w w C) 04 0) -4 Lf) C) (Z) ft a r (: " r- -4 CN 0 tm - C14 o 4 r, - " W - " M 41: CL 0) CT CN C14 CN CN CN CN CN m 1-4 -4 14 CN C13 C14 CN CN C14 r- OD Iq C14 (n Ln 1-4 -1 clq -0 Ln 113 In ,--I Ln -4 CN 1-4 00 1-1 a) 00 rr U') CT (N CN 'r 14 rq -4 Cq 1-4 -4 C) 1 0 1 C) 1 0 C; CD CD 1 1 C) C; CD (: Cl ( 1 1=1 : c, ff) C) I w C- -4 C) I w () -4 11-:r CN C) C> rl) -4 C) C) () 0 1-4 C) Cl) -4 (D 0 (1) -4 CD C) aD -i (1) W 14 Ul C) W 14 00 CD W W O CD CN o OD CN w OD 1,0 OD 10 14 I'D Olt C) ID a% (1) CD C) I 1 C4 w m rn 0 -4 "-zr co () co 1.0 ID 10 0) ON C14 1-1 O - 1-9 CY)CT C '! Llf) 1-4 I'D " -4 -4 L 1-4 ,.,:! C) 1 C) Cl) CT T C w a I-Ir 10 0 li C 1 0 rC14LI) Ul C) (1) OD CNrm 1--i I 1 ( r r- C14 r 1 co " ko 1-1 co 1-4 r- CN Ilzr OD Ln A -1 1-4 1-4 ( ( ( CD ( C 1 C 1 C, m -4 CD C) I I m -1 CD C) (C0 C r14 " 00 rl- 04 WI 43 .0 ID w C4 -4 00 CN Ln CN cn C4 w r- ID 'IO1.0 k.0 (14 m C> Lr) 00 O C 0 1 1 r- C) -0 4 (-) CD CD (1) C) wI co CN r- ao r CN 1-4, cq m CN clq rl) r- C 1! 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CD CD C C C a 1 C CD C) C C fn 1-4 C) C) :1) 1-4 D C) m O 1-4 CD (1) C) 1-4 C) rl) -1 CD 0 (n 0 CD (n O -4 CD cl Iq C) O Cl) -4 C) CD M C 1-4 C) -;:r CN CD C) (-) -I C> C) () -1 C) CD (1) CD 0) m 1.0 aD CN C> LO Lr) Ln r- CD m r- 0 co WI I'*- WI WI 10 w WI WI co -4 co 10 14 1-4 () -4 C) C) () -4 CD C) I r- I 04 I OD r- ell (1) 'IO 'IO 1 0 0 m c o r- 'IO N WI WI 0 C9 Ln r- o Ln 00 Ln (n 10 -:r Clq r- aD Cl) 14 co -o r- OD Ul t c ON Cq I'D co LI) -4 1-4 r2 (1) Cl) N o U') rl) r- C14 (:> cq tj) (11 C13 1.0 rcq a 00 -4 CN 1-4 I-* rl) W C14 ko cq ff! c r- N 'IO -0 C) CN N C C 0 (1) 0 clq CT 0 C n (1) Clq C C CD CD C D a ) C) C11 ( rl) O ( a co C> C) C14 00 CN C) CIA r a, C; -4 r- clq C> " a,, 1 "::! 1 (: C ( C C C CDCD -4 C) 0 C) -4 0 + -4 C) -4 C) + + + + + OD OD w C19 M co ID "M -IV r, Ln r co 'A C) -4 C) C) a C -4 Ln 1-4 C. 1-4 C) co C:) C) Ln ') r7 r- 0 C) Ln r- 'n (n LIC) Ln r- m Ln (1) Ln :D ct) ID 00 W (=) co 'o rCN 1.0 1-4 r 4 0 -4 0 0 0 ul r- 1-4 OD . 19 co CN 'A cq cq m 'IO OD0 0 clq OD0 C) 04 00 OD C) 1-1 a) 1-4 C14 rl) r-4 rq C) C,4 -4 cq -4 r- 00 'A CD ( C W 14 U') 1-4 C) 1-4 C) 0 -4 0 1-1 C) 1-4 CD -4 C> -4 C) A C) 14 CD Iq 0 -4 0 114 0 rM WI WI WI clq -0 Ln 14 'IO Ul CN 00 -4 00 C14 -1 00 OD --I CN (3) CD C w m 1-4 a) CD OD 14 M w CN CD (1) 1-4 r- C14 w CN r- (N ul -4 Ln -4 ID C14 r- cq Ln Lln C) n -4 I'd, C) CN -4 Ln C) Ul -4 -r C3 C14 1-4 ";r C) () -4 U-) C CT 14 1.0 C) U') 1 C> C C C. C CD a C) C) CD C C) CD C C ( C I-W U) 10 Ln " 0 C> C) C) C) 1w 10 ( C) C C) C C C C) C C CD 10 Ln I" Ln 'Ir Ln " C) C) C> CD CD a C> CD 0( 14 114 ON 10 a CN ao ko 1-4 C) C11 w m 1-4 0. cn a) q c (n "O C14 a) c ! 04 CN m 'o " CN -4 -4 Ln m w ko 10 04 r- cq w q C14clq 04 ONen _: o _ 7 ,-I Ln 10 CN CN 1-1 r- CN U')C) U-10 c ol C13 CN CN -4 co Ln C,4 'D 4 CN CN C4 1.4 ol 'o C'l CN (N l Ln r- F14 r- r- " Ln r- C) r, Ln OD Cl) r- -, C', U-) rr, cq C) . li -4 C) 1-1 D + C1 r+4 11 co O Ln CO m 1 .0 00 10 1-4 w -4 -4 O 1-1 CD 1-4 0 11 0 -4 CD -I CD -4 CD 1-4 C> 'A CD -4 C) WI 114 clq OD w co C) 00 1-4 0 114 C) w C) CN Ln CN Ln 1.0 (z -0 - LO C) V. -4 10 CD 1 1 1 1 (=! r- clq " Ul co -4 1.0 en oll tl- co -4 c c 1-1 Ln --I Ln 1-4 LA --I r- CIA r- rn w C 1-4 1 C> q 1-4 Ln CD q 14 -p C) q 14 ko C) Ln 1-1 0 0 r -4 C) C C C) 0 C C C C 0 C ( 1 C ( ( C 1 1 C; ( 1 O CD Ln 10 Ln "r a) Ilzr Ln I-zr Ln " Ln 10 LI) 10 C) 0 C) C) C) 0 0 C) C> C) 0 0 CD C) ko r- m 1-4 Ln r- m ul r u co -4 cq 04 -4 C14 C14 (N C14 Ln C14 w en m Ln 0, Cl) ON 04 m a 0) c -4 C,4 'D -4 " CN tmk ! -4 C,4 (z) 04 C14 -4 CN 1-4 C14 1-4 1-4 1.4 clq CN Ln 11 129 ( kg -I fn c C,4 -4 CD C) CD U') lw Ln Ir C C) c ') C) W W a% m ! tMc c .0 r' C4 r r4' 14' to W r' -4 r W W co (n (1) r- CA at ao cli 1-4 CN-0 OD ko CN 40 -4 CN 40 c) C) 40 'r w 40 -4 (n Clq 0 r- " 0) -4 " 0 k.0 zw 00 (1) 40 00 Ln m co WI r- m LI) 1-1 m o 1-4 C> r 14 WI 4 -0 -4 14 LI) r rLn U') U') w 1-4 14 o m OD Ch CD co -4 oll a) 1-41 Ln I c C) C C CN ON 04 r- -4 r- CN CN (n 1 1.0 r- C) 'IO 1.0 r- 10 CV r C) -0 CN 0 a ( C) CD C14 r- a al : 14 r14 114 " C C . r Ln q WI WI W Iq C+4 C14+ : li 0 C) C) C) ko A Cq C) C) (n r- 0 4 0 C) 10 r- co --q . C m -4 0 C r- m CT ! -4 1-4 C) WI 114 a -W ONv 1-1 In r- 00 C) 0 L( C14:W 10 ON 40 r- en :w cq CD . Ln 1-4 0, CNko a 1-1 m ko 0 0, ko ko 4 -4 0) . r 1-4 C) WI WI o CD OD r2 U') -4 WI WI m aD co O c -4 c:) CN w Ln -4 Ln 1-4 -4 4 0 00 l C) 'D -4 L.C) -4 O a C) OD CD C) C 0 0 l 'D 'n 'D (14 1 1 r4 + w w (1) CN 1 C l CD Ln ko C ( C) C) + 1 O O 0 co (,o 'D (1) q. -I 0 C C 0 0 oll C14 114 1 CN0) r- w (n co -4 CD C) I-zr 10 r4 l rao 0 "w ,-4 rm C! . 1 -4 -4 0 -4 Clq C V) (n CD OD C) Ui CN (1) . 1 l--q m co CN M -4 0 CD Ln r4 m Ln 0) 10 "! Ll m Clq m a r, r- W C4 I'D i ll C 114+ W 00 m 00 Ln 'A r- -! I C) -4 C) C) 14 a% OD ko : -4 1-4 Cl) CD C 0) CN co 0) -0 (1) C14 1-4 c) C) cq 00 Cl) C14 C) Ln CN cn -4 C) C) 10 CN CD CD r- 1-4 CN ( CT 0 (n C) C CN CN C) 01 r- m -4 0 0 co CN 1.9 191 ( (Do Clq oll co 1--f cl 1 C 14 W W Ln cq Cq C a 0 --;r 10 -4 co "! ( C C) W 14 m Cl) cq -V 0 C) C) 0 -4 OD W 1 : Clq clq CN C11 a a -1 CN 03 rl- C) 0 OD rq N C) 0 'IO rCN w 1 -! 1 .o clq 0 C) r- 00 C) 'IO ao -o C) clq 10 rq 0 C4 cq W I-zr co r- OD04 0 cl C q C) W (D W ID CD clq (14 m cn cq C CN C-) 14 cl -4 -4 CN 1 OD C) Ln " 1 -4 cn C) 14 W =) Clq ll ( r- Cl) CT O O LI) a) C141-4 -4 (14 1-4 ( C Ln -4 cq O W W r- (1) Ll Ln 1 -4 rn O r- OD (1) -4 C) (1) CD C 10 CN CD W W 1.0 r- 10 m w m (1) C, CN C) 1.0 C) aN : C 00 C) W 14 rl) ON C C) Ln ao -0 r- CD CD Cq C> (1) -, C C r- a CN ON CN cq 1-1 CN (1) r- C 11) CIA CD C) (1) cq n (N C) 1.0 w C CN C) 0) c! --I C C C13 ko C14 C cn C) () m ko OD -4 CD Cl) CN CD CD (14 'IO Ul Cl) OD CIA C> CD (1) " 0 0 00 ID C) Ln 1-4 r ID en -0 rn (7) CN -1 0 CD ( c) fn C) Ln r- OD Ln -4 m M (11 -4 C (: C In A 10 10 CD r C) m Cl (z a% C C r- C) ko r- * -P r CN 1 C C 1-4 (.,:) Cq cq C) rl) w Ch 0 m 1 1 CD C) 0) m al N r- () CIA cq (: 0 (14 N co 1 C (14 cq q c -4 Ln C14 C14 N 1 C El- co CN 14 CN -4 (N CN 'n -0 r -4 C4 CN CN 1-4 cq 14 C14 C14 (1) C'4 ol k .0 a -4 rl) 1-4 04 r' 1-4 " 04 Ln r' C14 CN CN Ln 1.0 .o (13 Lr) 1-4 " ,) c( U-) 1-4 C14 'IO :-4 -4 N (n 1 1 1 1 ` ` C) C C c:) CD CD ::) 1-1 C) () 1-1 (-) (1) a CD WIr ID Lr) (1) rl) CD C) WIWI r- (n r- 00 ,-* a:) () (11 1.0 I-zr co (n -4 1 r- (,q CN C) L A CD C) WIWI (:)) -* 0) C) r-- -'r o 1) -* -I 10 C) 10 (1) CD (n N rn CN C) -p U 00 - Id. -4 CN (1) LI) (N m r- -4 C14 (1) CD 'IO C14 N CD U-) C'N N C) LI) CN CN 1 ` ` ` 1 1 C CD CD c ` 9 ` 1 C 1 1 1 1 1 1 ` ` ` CD CD c 0 (D CD C) C) CD C C m -4 CD C) zr C14 (D CD m -4 C> C> (-) -4 C) C) m -4 0 C) (n -4 CD C) m a C) m 4 14 1 aN m OD co -1 14 14 r4' W W W W W W W 14' 14' w a% -4 14 -4 r- kD -0 co -4 m C) clq a) rl) -4 ID r- kD co -4 CN CN Ln C14 1-:0Ln ;:r -0 IV C> U-) C) ( "! 19 r 19 1 1 r '19 ( 1 1 -4 r- r- cq a% C'N ko -4 1.0 -4 r- c Li C r 4 C N (13 m ao 0 ID 10 m OC) c (1) CN C) C) (1) C19 CD C) () C) CN CD C) O l 0 0 -4 -4 kD OD 0) -4 00 1,0 04 -V Ul 00 C) 0) 0) ID Ln cq 'A ` c C C o ao -o r- CDen cn cn -i (n C) CN C) CD Irr CN CD C) cl) " CD C) rl) cq CD CD (1) cq CD C> 11 CN C) C> Lf) -Ir r4' O W C r- O O W .o CD Ln M -4 M 4 C) Ul 14 10 r C (D CN CD (1) CN C) CD cl) CN CD CD (1) CN C) CD 00 C) r- (N CD ko -;:r CD 1.0 C) ID 1-4 -4 Cq Ln r- aD ko m r- CN -4 C; 00 -4 Lr) r-4 r4' ON rLn r- 1.0 r CD r- 1 1 l 10 -4 'O () N : ` C> c:) cq t- (1) ON -4 r- Lc) r0 I li I C 1 r 1 -4 - M nJ " ) CIJ M -4 (11 CD CT m 1.0 00 r- ID aN m cl N ` 1 C. C C14 (1 " 1 1 C) c:) C 'IO 00 m (1) r- 04 co " C`q (14 1 1 C) C> 0) () I A 1 1-4 CN " 1 1 C C (3) Lr) 10 1.0 1.0 C', lZ C) cq " ` ` C) C) C`lq1-4 ( ` C) CZ) -0 1-4 CD r- Ln 0) 1-4 LI) CD c-4 -,o rl) C`q C ` CD CD 0) Ln CD (-) CN -4 ` , (D CD (n -1 CD 0 0 WI CN0 c,4 ko ) C-) -I C) C) 1 1 0) C14 0 CD CN m U) 00 OD (::) m a 1 r Lc) CT -4 1 1 C. CD m C "! ` 1 ( 00 (14 1-4 CD kD r- 1 r 00 (14 rl) CT 1 1 CD C) .J. ') C14 N C4 q ( ` C C) CN CD r14 WI r- "o o r- 1! ( 1-4 04 1 I clq (1) ON 00 1-1 0 C C N 0 CN C) C 0 . -! I C14 cn C:) C) CN CD c allm Co C> CN C) C'N C) CD c c:) 10 I'D c> 1-4 (D CD C 1-4 CN C) C) c c 1-4 CN 0 C) c C CD C> C'> c> 'A C. --I + + CD C) 0 C) C C; a% C`q CD C'N (D CIq (Da CD CD + CD C C al CD C14 C C + w r- 1. oC) .0 rl_4 co .0 Ln c) cc) clq CIq c M r- co u] "O + w + W r-n 1CD C U.) rl) -01.0 -T ON kD -T 00 " C) 10 m co -. 4 0) -1 -1 r 'D r- ww rl) cq "O ab 10 ") r- co (-) r u 10 ! + C4 w - '-4 n rn w -4 'IO CN -o "O r Cq '.0 c .- , CD 1- CD + C) ko " -, 04 (:,)U') a) Ul co 0) r- CD 1-4 10 14 Ln -4 1-4 1-4 -4 -4 Oc) C) (z) c ( w 'IO -4 co Ln "O -4 w co '4C) OD C C CD (S + w -4 Ln Ln M -4 r- -4 CD (:: Z c c + w > CD 1-4 Ul -4 -4 Iq al --I -4 CT C) C> C) CT w I'D CN m LI) Ln -I -V 1-1 1-4 C) C) 1-4 0 CD CN co 1 ll c O r 1-: Cq J) ('14 U') Ln -4 .o r- U') Ln c4 C) CD C c) c c C::) CD Ln o 14 -4 CN (1) C) 4 0 1-1 C 1- C OD U') w Ln w 1-4 k.0 r- r- 1 1 14 10 00 (1) -* m CD C,4 2 CN r- 'IO 00 w CIq Ul .;r CD C) 1-4 0 C C o CD C) 1-4 LI) 1-4 1-4 -4 0 0 1-4 -4 C0 -4 ko E w 1.0 C> 0 0 00 (n r- U) -cr 1-4 CN 7% 00 OD ko CN r- (1) -4 m m 04 -4 C> Ul Lt Ir U 1 1 0 ` ` c 1 Ln -i Ln Lf) r- CT r- CN o -o o n C) 1-1 0 Ln ko Ul C) 'A 1-4 CTC) C) c:) a C k-0 " r- u) c,4 4 w Ln C> 4 CD -4 C C-4 CD a C) C) CN "" r0) 04 clq Ln 1-4 c 0 C) 1-4 C) r- .r 4 C) co 1-4 C) C) + W C) 00 r- .c 00 r- cn 1 + (1) r- (1) a) r- (n .0 C) -4 C (D C) m a) a,, r- CD -4 C -:r rn C> w o -4 -4 0 C) 14 -4 -4 00 o D 0 -4 cl) c C) 1--i -4 CT 0 li 0 -4 -4 ON0% 1 ,--I 1-1 CN CNen --A Ln 0 0 co -4 aN 1-4 1-4 1-4 m Ul O U') 1-4 1-4 0) 0 m 1--i GO C c> I W w 0.,p a) cn C -4 c;) 0 c C; + CD C C 1.0 C`14 (n U) U) C) I-z:r U-) CD CD 1.0 I-) -M C) Ln co cl) 1-4 ('4 CIq --I 40 0 () -o to Q Ln OD Ln CD m zo (1) C> "P LS a r- C) -4 ` 0) (` -! co C,4 "N c) r- cq 'o (N C,4 1-4 C14 04 CN I-q -4 -4 CN 04 1--i (14 r- ft a 0) 10 0 14 (1) ko 14 C> 0, r- r- Li) CD w r CD CIq 10 rrzw 'IO r- :w m 0 CYN 'I o m a (n -4 L t7l 1! U-) 0) r- d. (,3 -0 Ul CD CD 114 r C19 rl) (1) r- C-4 (1) .0 U,) (D 0 Ln C. 0 ODM r- CIA (1) m m co CN -0 zw OD OD :* -o zw 10 1-1 zw 10 10 t, co C) a I'Dko aImr-, %.oa, tm`, R CD 04 li . CC) -4 CN -4 CN m q 00 IN "...4 " -0 Ln CD U) C) l I r- 041-4 rI CD OD 10 CD 1-4 10 r- 10 0 Ln C) a 0-0 :w -4 CN . %Da co (,Rc 04 -4 10 CD Ln C) -O. LO C> CD WI 114 co CN 0 m 1- m Lna) a co to 'I m Ira V! L -4 CN Im c 1 (14 1-4 CT -4 CT 1-4 -0 -0 -0 CN -4 CN 1-1 clq -4 . rl) (11 cn cn (1) Ln ID r- co 130. ID ID m Ln CD c 11 1--i CN zw Ln 10 :w ONr-0 :0 10 r- m 11 :w c-4 CD Ln 1-4 CT 1-4 CT 1-1 10 C> 0 Ln 10 cn 1-4 Oc) cc) Cq CN -4 , Ln C> Ln c,3 04 (1) (ID C,4 ,__I C,4 'o .0 CD cn CN LOOD R 191 a, r w CN 1-4 R -4M Ln 00 Cq 1-1 Ln C`14" w 1-4 CN CT 1-4 w 1-4 -0 r- CN 04 1-1 CC) w 0 9w APPENDIX D ONE GROUP BALANCE CHECK RESULTS The ratios of residual to total loss and total source are given in percent. 131 I 17 J 9 K 5 18 9 5 19 20 21 17 18 19 20 21 22 23 18 19 20 21 22 23 24 20 21 22 23 24 9 9 9 10 10 10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 12 12 5 5 5 17 18 19 9 9 9 6 6 6 20 21 9 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 17 18 19 20 21 22 23 18 19 20 21 22 23 24 20 21 22 23 24 10 10 10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 12 12 9 6 17 18 19 20 21 17 18 19 20 21 22 23 18 19 20 21 22 23 24 20 21 22 23 24 9 9 9 9 9 10 10 10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 12 12 7 7 7 7 7 17 18 19 20 21 9 9 9 9 9 8 8 8 8 8 17 18 19 20 21 22 23 18 19 20 21 22 23 10 10 10 10 10 10 10 11 11 11 11 11 11 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 TOTAL LEAKAGETOTAL ABSORP TOTAL LOSS 1.08633E-05 2.095OOE-05 3.18133E-05 2.041OOE-05 1.12020E-05 1.16479E-05 1.35869E-05 1.31283E-05 -5.79491E-06 1.29490E-05 -4.01155E-06 7.78670E-06 -9.12188E-06 2.16344E-06 -4.6260SE-06 8.06749E-06 1.32212E-05 7.81022E-06 -7.42257E-06 8.37898E-06 -9.59164E-06 1.15940E-05 -8.24828E-06 1.26277E-05 -7.19076E-06 1.20575E-05 6.60932E-06 7.38191E-06 2.45990E-05 2.09609E-06 2.42193E-05 1.30372E-05 -8.61004E-06 1.27270E-05 -1.08853E-05 1.18032E-05 1.97611E-05 1.10101E-05 2.07099E-05 1.13918E-05 -8.03719E-06 7.94306E-06 -4.61657E-06 1.32087E-05 2.36130E-05 1.32678E-05 2.44444E-05 9.58311E-06 2.36080E-05 1.03622E-05 -6.60220E-06 1.08546E-05 -2.72485E-06 1.25576E-05 2.65776E-05 1.22816E-05 -5.90344E-06 1.23370E-05 -6.49261E-06 6.8717SE-06 -2.37293E-05 1.79280E-06 -1.51755E-05 7.16104E-06 5.04393E-06 6.92675E-06 -7.47699E-06 7.61885E-06 -8.67323E-06 1.03229E-05 -8.95884E-06 1.20642E-05 -9.8910SE-06 1.09255E-05 -2.86092E-06 6.46613E-06 1.33206E-05 1.85618E-06 2.12792E-05 1.20845E-05 -9.98156E-06 1.19053E-05 -1.33766E-05 1.05066E-05 2.31005E-05 1.00783E-05 2.35470E-05 1.01177E-05 -9.84199E-06 7.26927E-06 -3.23655E-06 1.28250E-05 2.77566E-05 1.24779E-05 2.60302E-05 1.10048E-05 2.57992E-05 1.17673E-05 -7.86799E-06 1.23152E-05 -3.07869E-06 1.40929E-05 2.99518E-05 1.35498E-05 -7.00036E-06 1.32243E-05 -7.36828E-06 7.56406E-06 -2.50965E-05 1.84115E-06 -2.02804E-05 7.48752E-06 4.76907E-06 6.96884E-06 -7.80465E-06 8.20889E-06 -9.92454E-06 1.10832E-05 -9.56595E-06 1.33377E-05 -1.10068E-05 1.24710E-05 -5.05634E-07 6.7802SE-06 1.27223E-05 1.86113E-06 1.94527E-05 1.28591E-05 -1.24551E-05 1.33408E-05 -1.41471E-05 1.14762E-05 2.67750E-05 1.12103E-05 2.61484E-05 1.08184E-05 -1.10486E-05 7.86604E-06 -3.90860E-06 1.36494E-05 3.07936E-05 1.40726E-05 2.66442E-05 1.14001E-05 2.66448E-05 1.13212E-05 -5.60382E-06 1.23475E-05 -2.59271E-06 1.4320SE-05 3.06421E-05 1.42429E-05 -5.72001E-06 1.42476E-05 -7.66642E-06 8.08838E-06 -2.84972E-05 1.85003E-06 -2.42442E-05 7.42888E-06 6.94965E-06 7.29730E-06 -7.99573E-06 8.38803E-06 -9.30556E-06 1.14444E-05 -9.71859E-06 1.41975E-05 -9.93786E-06 1.31872E-05 -5.43385E-06 7.18465E-06 1.38520E-05 1.86351E-06 2.25806E-05 1.31591E-05 -1.21486E-05 1.37786E-05 -6.42744E-06 -3.57556E-06 2.27540E-05 TOTAL SOURCE 1.94863E-05 3.16120E-05 2.01796E-05 5.22051E-06 2.12275E-05 1-00113E-05 2.49896E-05 3.58823E-05 2.40741E-05 7.1540SE-06 2.3762SE-05 3.77515E-06 1.32785E-05 -6.95844E-06 1.41621E-06 3.44140E-06 1.35546E-05 2.10314E-05 1.32766E-05 9.56404E-07 1.47099E-05 2.0023SE-06 2.09093E-05 4.37944E-06 2.33096E-05 4.86677E-06 2.22283E-05 1.39912E-05 1.22043E-05 2.66951E-05 1.35015E-06 3.72565E-05 2.36150E-05 4.11694E-06 2.33770E-05 9.1782SE-07 2.13508E-05 3.07712E-05 1.98968E-05 3.21017E-05 2.04877E-05 -9.41279E-08 1.35962E-05 8.59213E-06 2.42926E-05 3.68809E-05 2.44539E-05 3.40275E-05 1.70681E-05 3.39702E-05 1.85004E-05 4.25236E-06 1.95216E-05 9.83276E-06 2.28537E-05 3.88592E-05 2.2182SE-05 6.43356E-06 2.24003E-05 3.79167E-07 1.16329E-05 -2.19365E-05 1.28631E-06 -8.01443E-06 1.19420E-05 1.19707E-05 1.16540E-05 1.41853E-07 1.3103SE-05 1.64963E-06 1.83260E-05 3.10539E-06 2.20103E-05 1.03446E-06 1.97556E-05 3.60522E-06 1.06424E-05 1.51768E-05 1.46716E-06 3.33637E-05 2.16485E-05 1.92369E-06 2.15582E-05 -2.87001E-06 1.86833E-05 3.31789E-05 1.79478E-05 3.36647E-05 1.80175E-05 -2.57272E-06 1.23813E-05 9.58847E-06 2.32752E-05 4.02345E-05 2.28011E-05 3.70350E-05 1.96793E-05 3.75664E-05 2.10515E-05 4.44726E-06 2.22223E-05 1.10142E-05 2.57593E-05 4.35016E-05 2.45186E-05 6.22393E-06 2.39699E-05 1.95785E-07 1.29726E-05 -2.32553E-05 1.509OOE-06 -1.27929E-05 1.25701E-05 1.17379E-05 1.16602E-05 4.04248E-07 1.4185SE-05 1.15862E-06 1.97253E-05 3.77171E-06 2.43609E-05 1.46423E-06 2.26040E-05 6.27465E-06 1.12659E-05 1.45835E-05 1.58005E-06 3.23117E-05 2.31253E-05 8.85691E-07 2.42177E-05 -2.67093E-06 2.04681E-05 3.79853E-05 2.00733E-05 3.69667E-05 1.93066E-05 -3.18259E-06 1.34951E-05 9.74077E-06 2.47310E-05 4.48662E-05 2.57638E-05 3.80442E-05 2.03562E-05 3.79660E-05 2.0237SE-05 6.74371E-06 2.22633E-05 1.17281E-05 2.61152E-05 4.48850E-05 2.58394E-05 8.52760E-06 2.58272E-05 4.21957E-07 1.38704E-05 -2.66472E-05 1.54710E-06 -1.68153E-05 1.25024E-05 1.42469E-05 1.22491E-05 3.92297E-07 1.45339E-05 2.1388SE-06 2.04160E-05 4.47895E-06 2.58520E-05 3.24929E-06 2.38041E-05 1.75080E-06 1.19919E-05 1.57155E-05 1.63858E-06 3.57397E-05 2.35882E-05 1.62999E-06 2.49782E-05 132 RESIDUAL 1.23269E-05 1.14325E-05 1.60070E-05 1.49783E-05 1.18082E-05 1.6608SE-05 9.50331E-06 8.37465E-06 1.01132E-05 7.75482E-06 1.37535E-05 1.89069E-05 1.89301E-05 1.73616E-05 1.7868SE-06 2.53449E-05 1.36415E-05 1.92601E-05 2.04330E-05 1.08744E-05 1.16140E-05 1.36904E-05 1.57005E-05 1.24270E-05 1.69594E-05 1.54699E-05 1.52693E-05 1.30209E-05 1.66764E-05 1.59667E-05 1.12537E-05 2.32228E-05 1.99565E-05 3.16644E-07 1.29619E-05 1.66764E-05 1.89050E-05 1.87212E-05 7.03719E-06 1.37097E-05 1.17152E-05 1.96345E-05 2.15533E-05 1.52310E-05 1.56472E-05 1.49540E-05 1.36867E-05 1.74334E-05 1.73557E-05 1.65149E-05 1.77750E-05 1.47451E-05 1.89830E-05 1.77460E-05 1.27769E-05 2.47643E-05 2.53630E-05 7.77308E-08 1.37816E-05 1.85666E-05 2.05892E-05 2.11398E-05 4.99124E-06 1.30034E-05 9.18645E-06 2.33320E-05 2.31390E-05 1.79120E-05 1.76601E-05 1.66777E-05 1.49903E-05 1.91025E-05 1.76881E-05 1.77283E-05 1.55196E-05 1.43871E-05 1.90457E-05 1.72996E-05 1.34485E-05 2.81943E-05 2.93178E-05 1.99783E-06 1.41416E-05 1.82771E-05 2.13731E-05 2.05548E-05 1.02411E-05 1.40769E-05 1.21515E-05 2.33482E-05 RESID/LOSS 3.87478E+01 3.61650E+01 3.06617E+02 1.49614E+02 3.29081E+01 2.32158E+02 2.51733E+02 -1.20352E+02 2.93868E+02 3.68725E+01 1.43804E+03 9.44221E+02 4.32250E+02 3.56737E+02 1.27714E+01 9.49423E+01 3.66151E+01 4.67824E+02 2.22623E+03 3.53395E+01 3.61789E+01 -1.45444E+04 1.82731E+02 3.36950E+01 4.98403E+01 4.55394E+01 3.59078E+02 1.32424E+02 4.29149E+01 2.48178E+02 2.96801E+03 -1.05864E+02 -2.49007E+02 2.64517E+00 9.13758E+03 1.01092E+03 6.08780E+02 1.80975E+03 1.95195E+02 9.03329E+01 3.51135E+01 1.02067E+03 -7.50983E+02 4.59058E+01 4.64796E+01 -5.81253E+02 1.42741E+02 4.33295E+01 4.68631E+01 4.39620E+01 3.99685E+02 1.33874E+02 4.36375E+01 2.85125E+02 6.52597E+03 -1.06489E+02 -1.98258E+02 6.62220E-01 3.40918E+03 1.60247E+03 5.45884E+02 1.44374E+03 7.95461E+01 8.91655E+01 2.84307E+01 2.63433E+03 -8.66330E+02 4.71551E+01 4.77730E+01 -5.24029E+02 1.53892E+02 4.25765E+01 4.64934E+01 4.66951E+01 2.30134E+02 1.22672E+02 4.24321E+01 2.02866E+02 3.18716E+03 -1.05806E+02 -1.74351E+02 1.40229E+01 3.60482E+03 8.54518E+02 4.77189E+02 6.32594E+02 5.84938E+02 8.95735E+01 3.40001E+01 1.43241E+03 RESID/SOURCE 6.32595E+01 5.66538E+01 7.54068E+01 5.99382E+01 4.90494E+01 6.98938E+01 7.15694E+01 5.91344E+02 7.46108E+01 5.84096E+01 9.34982E+01 9.04235E+01 8.12119E+01 7.81056E+01 1.46413E+01 1.87719E+03 5.77663E+01 8.23889E+01 9.57012E+01 5.46539E+01 5.66879E+01 1.00692E+02 6.46306E+01 5.08181E+01 9.93631E+01 8.36191E+01 7.82172E+01 5.69751E+01 7.51771E+01 7.12791E+01 9.67406E+01 1.80538E+03 1.67111E+02 2.71704E+00 9.89175E+01 9.09984E+01 8.58912E+01 9.47637E+01 6.61240E+01 9.34436E+02 5.41154E+01 9.10768E+01 1.15361E+02 8.48629E+01 8.68446E+01 1.20779E+02 5.88039E+01 7.64585E+01 8.81930E+01 7.84502E+01 7.99874E+01 5.72418E+01 7.74228E+01 7.40344E+01 9.84908E+01 1.64111E+03 2.01773E+02 6.66635E-01 9.71503E+01 9.41262E+01 8.45173E+01 9.35222E+01 4.43040E+01 8.22977E+02 3.97248E+01 9.63428E+01 1.13049E+02 8.92331E+01 9.14717E+01 1.23583E+02 6.06131E+01 7.41447E+01 8.68928E+01 8.76000E+01 6.97093E+01 5.50908E+01 7.37079E+01 6.69821E+01 9.69579E+01 1.82239E+03 2.34496E+02 1.63100E+01 9.73008E+01 8.95235E+01 8.26747E+01 8.63499E+01 8.54001E+01 8.59091E+02 5.15154E+01 9.34743E+01 24 20 21 22 23 24 17 18 19 20 21 17 18 19 20 21 22 23 18 19 20 21 22 23 24 20 21 22 23 24 17 18 19 20 21 17 18 19 20 21 22 23 18 19 20 21 22 23 24 20 21 22 23 24 17 18 19 20 21 17 18 19 20 21 22 23 18 19 20 21 22 23 24 20 21 22 23 24 17 18 19 20 21 17 18 19 20 21 22 23 18 19 11 12 12 12 12 12 9 9 9 9 9 10 10 10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 12 12 9 9 9 9 9 10 10 10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 12 12 9 9 9 9 9 10 10 10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 12 12 9 9 9 9 9 10 10 10 10 10 10 10 11 11 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 -1.483613E-05 2.82614E-05 2.76984E-05 -1.28208E-05 -3.71709E-06 3.20848E-05 2.53011E-05 2.58040E-05 -8.5015SE-06 -1.98645E-06 3.00989E-05 -4.40SOOE-06 -8.674OIE-06 -3.19039E-05 -2.426OOE-05 2.01653E-06 -8.89770E-06 -8.7574SE-06 -1.00787E-05 -1.403OIE-05 -3.34667E-06 1.26131E-05 1.82155E-05 -1.45835E-05 -1.30334E-05 2.62798E-05 2.54790E-05 -1.17250E-05 -2.28317E-06 3.01876E-05 2.15189E-05 2.20032E-05 -8.24839E-06 1.37552E-06 2.60188E-05 -2.92867E-06 -1.03184E-05 -3.25172E-05 -2.76469E-05 -5.85201E-07 -1.07706E-05 -5.590OOE-06 -6.46345E-06 -1.2809SE-05 -6.20587E-06 2.80865E-06 1.52782E-05 -1.35496E-05 -9.7311SE-06 2.21699E-05 2.3168SE-05 -1.55968E-05 1.28050E-06 2.62574E-05 1.90871.E-05 1.97922E-05 -8.90223E-06 2.87152E-06 2.28087E-05 -1.13411E-06 -9.56722E-06 -3.44563,E-05 -2.67593E-05 -8.43806E-07 -1.02465E-05 -5.31105E-06 -4.85946E-06 -1.28959E-05 -1.17102E-05 2.66142E-06 1.32990E-05 -1.26924E-05 -8.0241SE-06 1.94999E-05 1.95974E-05 -1.34105E-05 1.86110E-06 2.25413E-05 1.67038E-05 1.62438E-05 -9.44742E-06 1.77768E-06 2.06611E-05 -2.05727E-06 -9.16003E-06 -2.99752E-05 -2.82826E-05 -2.04286E-06 -1.03722E-05 -6.19429E-06 -4.47586E-06 -1.20159E-05 1.22933E-05 1.19469E-05 1.16609E-05 8.20863E-06 1.43853E-05 1.46471E-05 1.00849E-05 1.10184E-05 1.25221E-05 1.36102E-05 1.35784E-05 1.37338E-05 7.91776E-06 1.81442E-06 7.42659E-06 7.3443SE-06 8.43079E-06 1.1062SE-05 1.35430E-05 1.33476E-05 7.34757E-06 1.78577E-06 1.28045E-05 1.34109E-05 1.15210E-05 1.10075E-05 1.06175E-05 7.84928E-06 1.33574E-05 1.33693E-05 8.22003E-06 9.16972E-06 1.14647E-05 1.1036SE-05 1.12391E-05 1.18201E-05 7.31180E-06 1.7319SE-06 7.23026E-06 7.22951E-06 7.71212E-06 8.88607E-06 1.11341E-05 1.25913E-05 7.06128E-06 1.77459E-06 1.28461E-05 1.28175E-05 9.50501E-06 9.51364E-06 8.80277E-06 7.19622E-06 1.16602E-05 1.13757E-05 7.73382E-06 7.71669E-06 1.08329E-05 9.59607E-06 9.89685E-06 1.01055E-05 6.50099E-06 2.0400SE-06 7.33534E-06 6.9482SE-06 7.03473E-06 8.01106E-06 9.28794E-06 1.16551E-05 6.80690E-06 2.04745E-06 1.2314SE-05 1.14483E-05 7.73452E-06 8.04875E-06 7.79876E-06 6.85556E-06 1.05918E-05 9.83282E-06 6.09413E-06 7.02712E-06 9.88926E-06 8.16610E-06 9.2074SE-06 8.76696E-06 5.69119E-06 1.60914E-06 6.16961E-06 6.11071E-06 6.33373E-06 6.41497E-06 8.36550E-06 1.02616E-05 -2.54334E-06 4.02083E-05 3.93593E-05 -4.61217E-06 1.06682E-05 4.67319E-05 3.53860E-05 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9.82575E+01 9.06652E+01 1.14673E+02 1.79812E+02 3.18776E+01 9.66293E+01 7.88198E+01 6.82213E+01 9.35916E+01 3.35469E+01 4.45472E+01 5.72102E+01 1.08209E+02 1.47224E+03 1.50626E+02 1.79891E+01 22 23 18 19 20 21 22 23 24 20 21 22 23 24 10 10 11 11 11 11 11 11 11 12 12 12 12 12 16 16 16 16 16 16 16 16 16 16 16 16 16 16 -5.75871E-06 -2-71754E-06 -1.72124E-06 -5.91484E-06 -1.73394E-06 6.32173E-06 8.12292E-06 -6.43806E-06 -4.07764E-06 7.42412E-06 7.40386E-06 -6.70992E-06 1.04669E-06 8.96014E-06 Core total loss Core total source Core total residual Residual/Loss M Residual/Source 4.0063SE-06 3.92732E-06 4.44976E-06 5.92040E-06 3.94821E-06 1.40224E-06 7.01344E-06 6.07438E-06 3.84284E-06 3.95819E-06 3.94784E-06 3.36894E-06 4.79825E-06 4.39318E-06 = = = = (%) = -1.75233E-06 1.20978E-06 2.72852E-06 5.55773E-09 2.21427E-06 7.72397E-06 1.51364E-05 -3.63684E-07 -2.34803E-07 1.13823E-05 1.13517E-05 -30409SE-06 5.84494E-06 1.33533E-05 6.75721E-06 6.47830E-06 8.09392E-06 1.08377E-05 6.13564E-06 8.23216E-07 1.24116E-05 1.11407E-05 6.84582E-06 7.09508E-06 6.46655E-06 5.67047E-06 8.79883E-06 7.97567E-06 2.46031E-03 4.04258E-03 1.58228E-03 6.43122E+01 3.91402E+01 135 8.50954E-06 5.26852E-06 5.36539E-06 1.08321E-05 3.92137E-06 6.90075E-06 2.724SOE-06 1.15044E-05 7.08062E-06 4.28722E-06 4.88515E-06 9.01146E-06 2.95389E-06 5.37765E-06 -4.85613E+02 4.35494E+02 1.96641E+02 1.94901E+05 1.77095E+02 8.93421E+01 1.80017E+01 -3.16329E+03 -3.01556E+03 3.76657E+01 4.30345E+01 -2.69725E+02 5.05375E+01 4.02720E+01 1.25933E+02 8.13257E+01 6.62892E+01 9.99487E+01 6.39113E+01 8.38268E+02 2.19537E+01 1.03264E+02 1.03430E+02 6.04253E+01 7.55449E+01 1.58919E+02 3.35714E+01 6.74256E+01 APPENDIX E THE TEST OF HOMOGENIZATION PROCEDURE The files given in this Appendix are: hesap : MCNP results for one fuel element test run in which mult 1 = absorption reaction rate mult 2 = total reaction rate mult 3 = elastic scattering reaction rate inult 4 = ny) reaction rate mult =n sigma fission reaction rate inult 6 = fission reaction rate hes.f Cross section proccesing and neutron balance calculation program for the test. 136 Program: c hes.f c this program calculates neutron balance for a separated individual c fuel lement rhomboid. c character*1 adum character*18 adum2 integer celln real keff dimension fl(100),rra(100),rrt(100),rre(100),rrg(100) dimension rrn(100),rrf(100) dimensionscur(4),sflx(4) dimension are(2),vol(6),celln(100) c open(unit=8,file=lhesapl,form=lformattedl,status='old') open(unit=9,file=lhes.oul,form=lformatted',status=lunknown') c keff=0.03292 c c reading hesap c read(8,'(a)')adum do i=l.,2 + read(8,*)celln(i),fl(i),rdum,rra(i),rdum,rrt(i),rdum, rre(i),rdumrrg(i),rdum end do do i=3.,17 read(E.,*)celln(i),fl(i),rdum,rra(i),rdum,rrt(i),rdum, + rre(i),rdum,rrg(i),rdum,rrn(i),rdum,rrf(i),rdum end do do i18,93 read(g,*)celln(i),fl(i),rdum,rra(i),rdum,rrt(i),rdum, + rre(i),rdumrrg(i),rdum end do read(8,1 (a) )adum do i=1,4 read(8,*)idum,scur(i),rdum,sflx(i),rdum end do read(8,1(a),)adum do i=1,2 read(BI(alB,4xlpel3.5))I)adum2,are(i) end do read(8,'(a)')adum do i=1,6 read(8,'(al8,lpel3.5))Iend=99)adum2,vol(i) end do 99 continue flx=O. absr=O. totr=O. fnur=O. fisr=O. tvol=O. do i=1,93 if(i.ge.1.and.i.lt.3)vl=vol(1) if(i.ge.3.and.i.lt.18)vl=vol(2) if(i.eq.18.or.i.eq.33)vl=vol(3) if(i.ge.19.and.i.1t.33)vl=vol(4) if(i.ge.34.and.i.1t.64)vl=vol(5) if(i.ge.64)vl=vol(6) flx=flx+fl(i)*vl absr=absr+rra(i)*vl totr=totr+rrt(i)*vl 137 fnur=fnur+rrn(i)*vl fisr=fisr+rrf(i)*vl tvol=tvol+vl end do avgfl:K=flX/tVol siga=(absr+fisr)/flx sigt=totr/flx signu:=fnur/flx sigf=:Eisr/flx tleak:=(scur(l)+scur(2)+scur(3)+scur(4))/tvol tloss:=tleak+siga*avgflx tsour(-e=(l./keff)*signu*avgflx resid=abs(tloss-tsource) write(9,101)flx,absr,totr,fnur,fisr,tvol 101 format(2xlflx :,,lpel3.5,/,2x, + + + + + c labsr Itotr Ifnur Ifisr ltvol :,,lpel3.5,/,2x, :,,lpel3.5,/,2x, :Ilpel3.5,/,2x, :Ilpel3.5,/,2x, :,,lpel3.5,/) writei:9,100)avgflx,siga,sigt,signu,sigf,tleak,tloss,tsource, + residresid/tlossresid/tsource 100 format(2x,'avgflx :',lpel3.5,/,2x, + Isiga:,,lpel3.5,/,2x, + 'sigt:,,lpel3.5,/,2x, + Isignu:',lpel3.5,/,2x, + 'sigf :Ilpel3.5,//,2x, + Itleak:,,lpel3.5,/,2x, + Itloss:',lpel3.5,/,2x, + Itsource:,,lpel3.5,/,2x, + 'residual:,,lpel3.5,//,2x, + + stop 'resid/tloss:',lpel3.5,/,2x, Iresid/tsource :lpel3.5) end 138 " 0 1 M a, 00 M - 0 M IN M M 1 C1 10 .. -.. 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