dancoff mc

IRI-131-95-003

DANCOFF-MC - A Computer Program for Monte Carlo Calculation of Dancoff Factors in Irregular

Geometries

S. Fehér

Technical University of Budapest Institute of Nuclear Techniques

H-1521 Budapest, Hungary

and

P.F.A. de Leege

Delft University of Technology Interfaculty Reactor Institute

Mekelweg 15, 2629 JB Delft, The Netherlands

Delft, June 1997

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Program Abstract for Code Package DANCOFF-MC Version 1.0

1. Name of the program DANCOFF-MC: Monte Carlo Calculation of Dancoff Factors in Irregular Geometries.

2. Computer for which the program is designed and other machine version packages

available Program (subpackage) Original computer Test computer name DCMCD DEC AXP 5/266 DEC AXP 5/266 DCMCL IBM Pentium PC IBM Pentium PC DCMCR IBM Pentium PC IBM RISC/6000 3. Description of program or function

DANCOFF-MC program was designed to calculate, by Monte Carlo method, the Dancoff factor which is used to determine the flux reduction in resonance integral calculations. DANCOFF-MC allows almost arbitrary arrangement of cylindrical or spherical fuel elements: different fuel region diameters, clads and gaps with different sizes, annular rods, arbitrary positions of rods or spherical pellets, and different macroscopic cross sections for each fuel element and its clad are all permitted. Optionally, it is also possible to calculate the Dancoff factor in a lattice of ‘grey’, i.e., partially transparent, fuel lumps.

4. Method of solution

Calculation of Dancoff factors is based on its collision probability definition. The program calculates the probability that a neutron emitted isotropically from the surface of the fuel region of the fuel element under consideration will have its next collision in the fuel region of any other surrounding fuel element. This probability is calculated by Monte Carlo method which is equally applicable in simple and in complicated geometries. Using the Monte Carlo method in the case of DANCOFF-MC means to select randomly the position where the neutron is emitted and the direction in which it travels. The lengths travelled in different material regions and the transport probabilities along any given path are calculated according to analytical formulae.

5. Restrictions on the complexity of the problem

Fuel rods and pellets cannot be mixed in the same arrangement. The cylinders' axes must be parallelly positioned in rod arrangements. Calculation of ‘grey-effect’ for annular geometries is not available.

6. Typical running time

Being a Monte Carlo calculation, the running time depends on the required accuracy. The calculation of one Dancoff factor with 100,000 histories, providing typically a statistical accuracy not worse than 0.001, takes 1 to 3 s on a DEC AXP 5/266 computer and 15 to 40 s on a 133 MHz Pentium PC if the number of surrounding lumps taken into account lies in the range between 100 to 400.

7. Unusual features of the program 8. Related and auxiliary programs

9. Status 10. References

• S. Fehér, J.E. Hoogenboom, P.F.A. de Leege, and J. Valkó, "Monte Carlo Calculation of Dancoff Factors in Irregular Geometries", Nucl. Sci. Eng., 117, 227-238 (1994)

• S. Fehér and P.F.A. de Leege, "DANCOFF-MC - A Computer Program for Monte Carlo Calculation of Dancoff Factors in Irregular Geometries", IRI-131-95-003, Delft University of Technology, Interfaculty Reactor Institute, (June 1997)

11. Machine requirements

DANCOFF-MC runs on DEC AXP, IBM RISC/6000, and IBM compatible personal computers. The main storage (RAM) requirement depends on the number of neighbouring lumps taken into account. Typical problems need 500 kbytes of main storage.

12. Programming language used

The code was written in FORTRAN-77 and compiled by DEC FORTRAN Version 6.3 on DEC AXP 5/266, by Lahey FORTRAN F77L3-EM/32 Version 5.10 on IBM Pentium PC, and by AIX XL FORTRAN Version 2.3 on IBM RISC/6000.

13. Operating system under which program is executed

DEC OpenVMS Version 6.2 on DEC AXP, MS-DOS 6.22 on IBM Pentium PC, and IBM AIX Version 3.2 on IBM RISC/6000.

14. Other programming or operating information or restrictions 15. Name and establishment of authors

• S. Fehér Technical University of Budapest, Institute of Nuclear Techniques Budapest, Hungary, and

• P.F.A. de Leege Delft University of Technology, Interfaculty Reactor Institute Delft, The Netherlands.

16. Material available (contents of code package)

Included are the second referenced document and source files, sample inputs, and outputs. 17. Categories

Keywords Monte Carlo method, Dancoff factor, reactor physics, fuel rods, fuel spheres, irregular lattices.

CONTENTS

1. Introduction 7

2. Algorithm of the DANCOFF-MC 9

3. Calculation of the ‘grey’ effect 11

4. Structure of the program 12

5. Input/output of the subroutine DCMC 14

6. Input/output of the subroutine DCMCI 15

7. Sample inputs and outputs 16

8. References 17

Appendix 1. DANCOFF-MC in SCALE-4 18

Figures 20

Tables 36

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1. INTRODUCTION

The program DANCOFF-MC has been developed to calculate, by Monte Carlo method, the Dancoff correction factor, which is used to determine the flux reduction in resonance integral calculations.

The Dancoff correction factor (or simply Dancoff factor) has two, equivalent definitions. The first one (the original or ‘historical’ one) was formulated by Dancoff and Ginsburg [1], who pointed out that in a closely packed lattice the in-current of resonance neutrons into the fuel is reduced, as compared to the in-current into a single fuel rod in an infinite moderator, because of the shadowing effect of adjacent rods. The relative reduction of the in-current is called the Dancoff correction. The second definition, which is more commonly used nowadays, is related to the method of collision probabilities [2]. According to this definition the Dancoff factor (C) is the probability that a neutron emitted isotropically from the surface of the fuel region of the fuel element under consideration will have its next collision in the fuel region of any other surrounding fuel element.

The Dancoff correction factor is one of the long-lived concepts of reactor physics. The concept was born more than fifty years ago and it came into the front of interest in the late 50s and 60s, when numerous papers presenting various methods and algorithms for calculation of the Dancoff correction were published. Many computer programs and algorithms being used even today for calculating Dancoff correction [3-5] are originated from this ‘boom’ of the topic. These programs, however, in order to limit the required computer time, are based on certain analytical methods and contain further geometrical simplifications. An additional deficiency is that these programs are capable of calculating Dancoff correction only for regular (square or triangular) lattices of fuel rods. Later the research on pebble-bed-reactor resulted in a few computer codes allowing to calculate Dancoff factors for three-dimensional lattices of fuel spheres [6,7]. From the 70s the increasing power of computers made it reasonable to apply the Monte Carlo method for Dancoff correction calculations. (Previously the Monte Carlo method, in this field, was usually used only for checking the validity of analytical procedures that calculated Dancoff corrections.) The number of papers reporting about such type of calculation is comparatively high, however, the computer codes used for these calculations are practically not available.

During the last two decades the topic of the Dancoff correction remained in the background, and probably this is the reason why the accuracy of computing the Dancoff factor has not improved sufficiently, while the accuracy of the modern reactor physics code systems has become much better than it was some two decades ago. Especially in the case of complicated and irregular geometries, the inaccuracy of the applied Dancoff correction as a source of overall error deserves examination. An additional complication is that present-day reactor physics code systems generally provide for the automatic calculation of the Dancoff correction, and the user is not always aware of the degree of approximation involved or the validity of the method in the actual application. It turned out that some of the commonly used algorithms are inaccurate even in infinite regular lattices [8].

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In some cases, mainly when the fuel geometry is rather complicated, the Dancoff factor is not calculated automatically by the code systems (as it is with the SCALE system [9] in the case of multiregion cell option); they have to be given as input. Such an example is the Canada deuterium uranium (CANDU) reactor [10], where bundles are arranged in a square lattice, each bundle being a tightly packed irregular array of 37 fuel pins. It is quite obvious that pins in symmetrically different positions require different Dancoff factors.

To provide a general solution to the problem, the DANCOFF-MC program, based on the Monte Carlo method, has been developed to obtain Dancoff factors in an arbitrary arrangement of cylindrical fuel pins or spherical fuel pellets. The DANCOFF-MC is of high generality: different fuel region diameters, clads and gaps with varying sizes, annular rods, arbitrary positions of rods or pellets, and different macroscopic cross sections for each fuel element and its clad are all allowed. (Rods and pellets cannot be mixed in the same lattice.) Optionally, it is also possible to calculate the Dancoff factor in an arrangement of ‘grey’, i.e., partially transparent, fuel lumps.

The program calculates the Dancoff factor using the collision probability definition. Neutrons are started from the surface of the fuel lump and tracked until they intersect another fuel lump, or, in the case of ‘grey’ fuel, until they escape from the region of interest. Using the Monte Carlo method in DANCOFF-MC means to select randomly the position where a neutron is emitted and the direction in which it travels. The lengths travelled in different material regions and the transport probabilities along any given path are calculated according to analytical formulae.

The DANCOFF-MC code has been written in Fortran 77 and has been tested on IBM compatible PC, IBM RISC/6000, and DEC AXP computers. Executable for PC was created with the Lahey F77L3-EM/32 v5.1 compiler. The code package includes the source program (with different random number routines for different computers) and several sample inputs and corresponding outputs.

Concerning the structure of the code it is important to note the following. Actually, the DANCOFF-MC program is a large general subroutine, called DCMC, which realises all the program features mentioned above. In order to calculate the Dancoff factor for a given arrangement, this subroutine (DCMC) is to be parametrised and called. This means that for a particular problem the user has to prepare the adequate calling (main) program. However, the code package of DANCOFF-MC includes two calling programs as examples of the usage of DCMC, as well. One of them is of high practical value because it calculates the Dancoff factor for regular (infinite) lattices of cylindrical fuel rods or spherical fuel pellets. (This program actually consists of a subroutine, named DCMCI, which calls DCMC; and a main program calling the subroutine DCMCI.) The second example included in the package is the DCMC37 program. This serves, first of all, as an illustration: it shows how to call the DCMC to calculate the Dancoff factors for the five, symmetrically different fuel rod positions in the CANDU PHWR 37 element fuel bundle.

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2. ALGORITHM OF THE DANCOFF-MC

As Monte Carlo type calculations are based on modelling the actual neutron histories, the Monte Carlo calculation of the Dancoff factor assumes a physical model of neutron transport in the given geometry. In our case, it is the process leading to the modified escape probability that is modelled, rather than the shadowing process.

Correspondingly, the algorithm of DANCOFF-MC calculates the probability that a neutron emitted isotropically from the surface of the fuel region of the fuel element under consideration will have its next collision in the fuel region of any other surrounding fuel element. In the case of ‘black’ fuel (i.e., if the total macroscopic cross section of the fuel is considered infinite), this probability is equal to the chance that a neutron started from the surface of the fuel region of one fuel element enters the fuel region of any other fuel element without having a collision with nuclei in the moderator or in the clads.

Assuming ‘black’ fuel and constant source strength of the emerging neutrons on the whole surface of the fuel region the Dancoff factor can be calculated as

C = d n - t l , - l ,

d n

MM

,C,da a a

da

tC i

i

n

i

C

•

•

=Ω Ω Ω Ω

Ω

exp [ ( ) ( )]Σ Σ1

Ω (1)

where , ,l l l lM C i G jj

n

i

n GC

+ + ===

11 = length of a vector ( l ) leading from the surface

point a of the fuel region of the fuel element under consideration through the moderator and possibly clads in the direction Ω to the surface of another fuel region

M = moderator C = clad

G = gap

nC = number of the clad-crossing segments along l (segments of l being inside a clad region)

lC,i = length of the i-th clad-crossing segment

Σ tC i, = total macroscopic cross section of the clad at the i-th clad-crossing

segment

nG = number of gap-crossing segments along l

lG,j = length of the j-th gap-crossing segment

n = normal vector of the surface at point a

Σ tM = total macroscopic cross section of moderator.

The integrals extend in Ω over all angles n ⋅⋅⋅⋅ Ω > 0 and in a over the fuel region surface of the fuel element under consideration.

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Using the Monte Carlo method in our case means to select randomly the position where the neutron is emitted and the direction in which it travels. The lengths travelled in different material regions and the transport probabilities along any given path are calculated according to analytical formulae. Instead of performing the integration in Eq. (1), which is a difficult task if the geometry is kept almost arbitrary, the required probability is obtained by averaging the values calculated along the randomly selected trajectories.

The general scheme of calculation in the case of parallel cylindrical fuel elements is shown in Fig. 1. (The case of spherical geometry is quite similar, the differences are discussed at the end of this section.) A point of emission A is selected uniformly at the surface of the fuel rod. The direction of the neutron flight ΩΩΩΩ is selected using a probability density for the cosine of the angle extending from ΩΩΩΩ to the normal n at the surface proportional to n • ΩΩΩΩ according to the factor in the integrand of Eq.(1) and using a uniformly distributed azimuth angle in the plane perpendicular to n. (This angular distribution is often referred to as cosine-current.) Then it is examined in which other rods the fuel region is crossed by the flight path. The distance to the nearest pin, AB*, will be the required flight distance. As the flight path goes through clad regions and gaps between fuel and clad, the path lengths in the clad and in the gap are also evaluated. Using the macroscopic total cross sections of moderator and clads, the exponential attenuation factor gives the probability that a neutron which passes through moderator and clad regions eventually reaches the surface without collision. The probability is recorded and averaged over the different points of the emitting surface and over the different flight directions. Note again that this description refers to the case of ‘black’ absorbers.

Some details of the algorithm described above are illustrated in Fig. 2, 3, 4, 5, and 8. Fig. 2 shows the geometry of the two-rod basic algorithm in a plane perpendicular to the rod axes. Fig. 3 illustrates the method which is used to select a neutron flight direction. In Fig. 4 the flow chart of the whole two-rod basic algorithm is shown and shortly commented. In Fig. 5 the geometry of the general case of parallel cylindrical fuel rods with clad and gap can be seen. Fig. 8 illustrates that a neutron may cross many clads before entering the first fuel region.

The algorithm of DANCOFF-MC makes use of some properties of the problem which simplify the calculation. In the case of cylindrical geometry only the flight direction is drawn in three-dimensional space, the rest of the calculation of path geometry is performed in two dimensions in the plane perpendicular to the axes of the rods, and the final results are projected back to the true direction. Target fuel elements which are inaccessible along a given path direction are rejected at an early stage of the calculation. The sign of the inner product of AO2 and ΩΩΩΩ xy is examined and only positive values are admitted. Along a flight path crossing a fuel element, the distances travelled in moderator, clad, gap or fuel are determined using the easily calculated distance t , without calculating the co-ordinates of any penetration point (see Fig. 2 and 3, and the flow chart in Fig. 4).

As it has already been mentioned, the scheme of calculation in the case of spherical geometry is rather similar to the cylindrical one. The main difference is in the selection of neutron emission point: In the case of spherical geometry the emission point is selected uniformly at the surface of a sphere. Further slight differences are related to the fact that in the case of spherical geometries the calculation of path lengths is mainly performed in three dimensions, although most of these calculations are performed in planes containing

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the path and the centre of the target sphere. In Fig. 6 the geometry of calculation in the general case of fuel spheres with clad and gap can be seen, while in Fig. 7 the flow chart of the two-sphere basic algorithm is shown and shortly commented.

3. CALCULATION OF THE ‘GREY-EFFECT’

When calculating the Dancoff correction, the assumption of ‘black’ fuel is quite general. Therefore in most cases the method described in the previous section provides sufficiently accurate result. However, if the fuel is not so ‘black’ (i.e., its total macroscopic cross section is not so large or the sizes of fuel lumps are small), there is a finite chance for neutrons to cross a fuel lump without having a collision inside it.1 In such a case the Dancoff correction must take into account this ‘grey-effect’, too, according to the general definition of the Dancoff factor given earlier.

Therefore, in the DANCOFF-MC it is optionally also possible to calculate the Dancoff factor in a lattice of ‘grey’, that is partially transparent fuel lumps. For this option the basic algorithm is modified to allow neutrons to pass through repeatedly fuel regions as well as through moderator, gaps and clads. The probability of getting absorbed in fuel is obtained by summing up the probabilities for each of the fuel regions crossed by the path. To account for the transparency of the fuel lumps, the following expression should replace the exponential in Eq. (1):

e e e ea b a b− − − −− + − +1 1 2 2 (1 ) [ (1 ) ] . . . (2)

where

a l ll

tC

C tM

M tC C

11

1 12 2= + +Σ Σ Σ,

, ,, ,

2 ,

a ll

ll

i tF i

F i tC i C i

tM

M i tC i C i= + + +−

−− −Σ Σ Σ Σ,

,, ,

,, ,1

11 1

2 2 , i = 2, . . . , n

and

b li tF i

F i= Σ ,, , i = 1, . . . , n ,

where n is the number of fuel elements crossed. Indexing such as C,i, M,I, and F,i refer to segments in coolant, moderator, and fuel, respectively, where i counts the fuel elements crossed, with i = 0 referring to the element of origin, i = 1 to the first element crossed, etc. (see Fig. 9). Σt is the total cross section and l is the length of path in the given region.

1 This is the case, for example, in a fluidised-bed-reactor, where the fuel regions of the pellets have a

diameter about a few tenths of a millimetre.

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One has to be careful, however, when using ‘grey’ Dancoff factors in certain reactor physics code systems. Some of these code systems require ‘black’ Dancoff factor because they include themselves (as SCALE does) a correction for the partial opacity of the fuel. These corrections are usually only approximate, and their use is limited to uniform lattices. A more general treatment could make use of the ‘grey’ Dancoff factors calculated exactly by DANCOFF-MC.

4. STRUCTURE OF THE PROGRAM

The main part of the DANCOFF-MC program is a large general subroutine, called DCMC, which realises all the calculations and program features mentioned in the above two sections2. In order to calculate the Dancoff factor for a given arrangement, this subroutine (DCMC) is to be parametrised and called. This means that for a particular problem the user has to prepare the adequate calling (main) program. Description of the input/output parameters of the subroutine DCMC is given in Table 1. and the parameters are shortly commented in the next section. DCMC requires the following subroutines:

DCMCCK which is to check the input parameters of DCMC;

SORT sorts real numbers is ascending order;

RNDIN initialises random number generator by the system time;

RNDINC initialises random number generator by a constant for test purposes; and

RNDS which is a general subroutine calling indirectly the computer (compiler) specific random number generator.

The last three routines (RNDIN, RNDINC, and RNDS), which are commonly called as ‘random routines’, have to be given specifically for any computer (compiler) specific version of DANCOFF-MC.

Descriptions of the DCMCCK and SORT subroutine can be found in Table 2 and 3, respectively. Since the ‘random routines’ are computer (compiler) specific programs, there is not description given for these routines in this documentation. Regarding to possible realisations of the ‘random routines’ we refer to the DANCOFF-MC code package itself, which includes three versions of these routines for DEC AXP, IBM RISC/6000, and IBM compatible personal computers (with Lahey compiler).

2 In a certain view we can say that the DANCOFF-MC program actually means this subroutine (DCMC),

and all the other parts of the DANCOFF-MC package are utility and sample programs to illustrate how to use the DCMC subroutine.

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The code package of DANCOFF-MC includes two calling programs as examples of the usage of DCMC, as well. First one is the program DCMCI, which actually is also a subroutine. This DCMCI routine is of high practical value because it calculates the Dancoff factor for regular (infinite) lattices of cylindrical fuel rods or spherical fuel pellets. Description of the input/output parameters of this subroutine (DCMCI) is given in Table 4. and the parameters are shortly commented in the 6. section. Main program calling the DCMCI is also included in the code package DANCOFF-MC in three version (DCMCIMD, DCMCIMR, and DCMCIML), respectively for DEC AXP, IBM RISC/6000, and IBM compatible personal computers (with Lahey compiler). The complete programs for calculating Dancoff factor in regular (infinite) lattices (i.e. the main segment and all the subroutines, required by the program, merged together into one file) are called DCMCID, DCMCIR, and DCMCIL, respectively for the three computer types mentioned above. These program versions differ from each other only in a few statements in their main segments and in the ‘random routines’. Structure of these programs can be shown schematically as follows:

The second calling program example included in the code package is the DCMC37 program. This serves, first of all, as an illustration: it shows how to call the DCMC to calculate the Dancoff factors for the five, symmetrically different fuel rod positions in the CANDU PHWR 37 element fuel bundle [10].

The cross section of a CANDU fuel bundle consisting of 37 cladded pins and surrounded by pressure tube, gas gap and calandria tube, is shown in Fig. 10. It is quite obvious that pin positions, marked A-E in Fig. 10, have different Dancoff factors. Since this bundle geometry has nor rectangular neither hexagonal symmetry, it seems to be a good example to present the applicability and advantages of DANCOFF-MC method compared to other Dancoff codes.

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Similarly to the case of DCMCIx programs, the code package DANCOFF-MC includes also three versions for main segment of the DCMC37 program (DCMC37MD, DCMC37MR, and DCMC37ML) and three complete programs (DCMC37D, DCMC37R, and DCMC37L) respectively for DEC AXP, IBM RISC/6000, and IBM compatible personal computers (with Lahey compiler). These program versions, like to the case of DCMCIx programs, differ from each other only in a few statements in their main segments and in the ‘random routines’. Structure of these programs can be shown schematically as follows:

The function of auxiliary routines and other program items, not mentioned here, is shortly described in Table 6, which is a summary of the components of code package DANCOFF-MC.

5. INPUT/OUTPUT OF THE SUBROUTINE DCMC

Description of the input/output parameters of the subroutine DCMC is given in Table 1. From this description it can be seen that DANCOFF-MC allows almost arbitrary arrangement of cylindrical or spherical fuel elements: different fuel region diameters, clads and gaps with different sizes, annular rods, arbitrary positions of rods or spherical pellets, and different macroscopic cross sections for each fuel element and its clad are all permitted. Optionally, it is also possible to calculate the Dancoff factor in a lattice of ‘grey’, i.e., partially transparent, fuel lumps.

Restrictions are only the following: (1) fuel rods and pellets cannot be mixed in the same arrangement; (2) the cylinders' axes must be parallelly positioned in rod arrangements; and (3) calculation of ‘grey-effect’ for annular geometries is not available.

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According to the design of the DCMC user must specify several geometrical and cross sectional data for all the lumps he wants to include in the calculation. NLUM is the (input) number of lumps (rods or pellets) taken into account in the calculation. Characteristics of the lumps have to be given in input vectors of length NLUM. First such vector among input parameters of DCMC is the vector XCENT containing the x co-ordinates of the centres of fuel rods or pellets. These co-ordinates can be stored in XCENT vector in arbitrary order by the user. However, in the further vectors specifying other lump characteristics the user must follow the same sequence he used in the vector XCENT.

The DANCOFF-MC allows to calculate Dancoff factors for arrangements of annular fuel rods or pellets (in case of IANNUL = 1). The terminology ‘annular’ in this context means that the fuel rod or pellet includes some moderator in its inner part (and possibly inner clad and gap, too), as it is shown in Fig. 11. This Figure helps the user to understand the meaning of input parameters RFLI, RGPI, and RCLI. If the input parameter IANNUL = 0, then DCMC calculates for ‘non-annular geometry’. However, outer clads and gaps of fuel rods or pellets are allowed even in this case.

DCMC allows to calculate more than one Dancoff factor simultaneously, i.e. Dancoff factors for different fuel rods or pellets in the given arrangement. The (input) number of lumps for which Dancoff factor is to be calculated, must be specified by the (input) parameter NDANF. The indices of the lumps for which Dancoff factor is to be calculated have to be stored in the (input) vector INDANF. The indexing of the lumps must be the same as used in the vector XCENT.

Main output parameters of the DCMC is/are the Dancoff factor(s) calculated (returned in the DANF vector) and its/their standard deviations (returned in the SDEV vector) . In the output vector NCEX the subroutine returns the numbers of Monte Carlo cycles executed for the calculation of the related Dancoff factors. The sequence of these numbers corresponds to the sequence of the Dancoff factors in the vector NDANF. If the program finds any error in input parameters, it returns an error code and stops. The meaning of these error codes are also given in Table 1.

6. INPUT/OUTPUT OF THE SUBROUTINE DCMCI

As it was mentioned above the subroutine DCMCI has two functions: it serves as an illustration of the usage of DCMC and it is a useful program at the same time. DCMCI calculates Dancoff factor for (infinite) regular lattices of cylindrical fuel pins or spherical fuel pellets. Description of the input/output parameters of the subroutine DCMCI is given in Table 4.

In the case of cylindrical geometry two types of rod lattices can be calculated by DCMCI: square and triangular (hexagonal) lattices of cylindrical fuel rods (ILATTI = 1 and 2, respectively). In the case of spherical fuel pellets three different arrays of pellets are allowed. These arrays are illustrated in Fig. 12, 13, and 14. Fig. 12 shows a cubic array (ILATTI = 3). Second array, presented in Fig. 13, has different names: it is called as rhombohedral or dodecahedral or hexagonal close-packed array (ILATTI = 4). Third

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lattice (Fig. 14) is called orthorombic or column hexagonal array (ILATTI = 5). It must be noted, however, that these Figures show special cases, namely arrays being as tight as possible, where the pitch of the array equals to the outer diameter of pellets. Of course, using CDMCI one can calculate less tight arrays, as well.

Probably the most particular input parameter of the DCMCI routine is the real number called ENVIR. This input parameter specifies the radius of environment to be taken into account. ENVIR must be given in terms of pitches, i.e. the real radius of environment is ENVIR*PITCH, where PITCH means the pitch of lattice (in centimetres). The DCMCI extends the calculation for the lumps (rods or pellets) centres of which are located inside the environment. If the centre of a surrounding lump is inside the environment, whole body of this lump is taken into account, even if a certain part of this lump is outside the environment. The usage of ENVIR is illustrated in Fig. 15 and 16 on a square and a triangular (hexagonal) lattice of fuel rods. Since lattices calculated by the DCMCI are regular, this usage of ENVIR results in a symmetric environment. The number of lumps taken into account by DCMCI increases with the second power of ENVIR in the case of rod-lattices, and with the third power of ENVIR in the cases of pellet-arrays. DCMCI returns the number of lumps (rods or pellets), which were included in the calculation, in the output parameter NLUM.

7. SAMPLE INPUTS AND OUTPUTS

The code package DANCOFF-MC includes 4 sample inputs and related outputs for the DCMCIx programs; and 2 sample inputs and outputs for the DCMC37x programs. The problems illustrated by these sample programs are the following: (1) square lattice of rods, (2) square lattice of ‘grey’ rods, (3) hexagonal lattice of annular rods, and (4) close packed lattice of spherical pellets for the DCMCIx programs; and the CANDU 37-element fuel bundle with two different moderators for DCMC37x programs. The inputs are the same for all the three program versions (running on DEC AXP, IBM RISC/6000, and IBM compatible personal computers with Lahey compiler). Sample inputs are shown in Tables 7 to 12.

In order to help the user in preparing further inputs the input data are commented in the sample input files. The name and a short description of the input data, as well as a character showing its type (I = integer, F = floating) are given in the first 60 character positions preceding the data. However, these information is skipped by the program and only the actual input data are read beginning from the 61st character positions. Actual data can be given in free format in the field of 61 to 80 positions.

Output files generated by different program versions are marked with an extra D, R, or L character at the end of their file names (preceding the .OUT extension), accordingly to the computer platforms mentioned above. Sample outputs are shown in Tables 13 to 30.

Table 6 gives an overview on the files included in the code package DANCOFF-MC. Tables 31, 32, and 33 list the files packed in the DCMCD, DCMCR, and DCMCL subpackages, respectively.

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8. REFERENCES [1] S.M. DANCOFF and M. GINSBURG: “Surface Resonance Absorption in a

Close-Packed Lattice”, CP-2157 (Oct. 1944). [2] G. I. BELL and S. GLASSTONE: Nuclear Reactor Theory, Chap. 2.8, Van

Nostrand Reinhold Company, New York (1970). [3] H. GELLINGS and A. SAUER: “Programmbeschreibung zu Dancoff Jr., IBM

7040”, Allgemeine Elektricitäts-Gesellschaft, Report KEA-114 (1963). [4] A. SAUER: “How to Use the Code DANCOFF-III: A Computer Code for the IBM

7040”. Allgemeine Elektricitäts-Gesellschaft (July 1966). [5] I. CARLVIK: “The Subroutine DASQHE”, Appendix II in “The Dancoff Correction

in Square and Hexagonal Lattices”, Nucl. Sci. Eng., 29, 325 (1967). [6] J.R. KNIGHT: “SUPERDAN: Computer Programs for Calculating the Dancoff

Factor of Spheres, Cylinders and Slabs”, ORNL/NUREG/CSD/TM-2, RSIC/PSR-282, Oak Ridge National Laboratory (Mar. 1978).

[7] J.P. MCNEECE, T.J. TRAPP and J.K. THOMPSON: “MCDAN: a Monte Carlo

computer code for calculating the Dancoff correction factor for spheres and rods”, PNL-3086, Battelle Pacific Northwest Laboratories (Aug. 1979).

[8] S. FEHÉR, J.E. HOOGENBOOM, P.F.A. DE LEEGE and J. VALKÓ: “Monte

Carlo Calculation of Dancoff Factors in Irregular Geometries”, Nucl. Sci. Eng., 117, 227 (1994).

[9] “SCALE-4: A Modular Code System for Performing Standardized Computer

Analyses for Licensing Evaluation”, NUREG/CR-0200, ORNL/NUREG/CSD-2/R4, RSIC/CCC-545, Rev. 4, Oak Ridge National Laboratory (1990).

[10] “CANDU Nuclear Generating Station Technical Summary”, Atomic Energy of

Canada Limited, Sheridan Park (1991).

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APPENDIX 1: DANCOFF-MC IN SCALE-4

The DANCOFF-MC code package can be included in the SCALE-4 code system to determine a Dancoff factor using Monte Carlo methods. The Dancoff factor determined by the Monte Carlo method is more accurate than the factor determined by the build in procedure due to the approximations used in the build in procedure. CPU time is increased using the Monte Carlo method. For instance, on a DEC AXP 5/266 computer the MC method uses 10 seconds while the build in one uses 1 second. Adaptations are available for the MIPLIB subroutines which are linked to the control module CSAS4. DANCOFF-MC is included as a subroutine callable package named DCMCISP. This package includes the subroutine DCMCIS (see Table 5) and all other subroutines required by DCMCIS. In the SCALE-4 the following call is used for DANCOFF-MC: CALL DCMCIS (NCTP, ENVIR, IGP, ICL, PITCH, FUELOD, TKMOD2, CLADOD, CLADID, STCLU, STMD, STMDIU, NCYCLE, SACCUU, DANFU, IER). For a full description of these arguments used see Table 5. Some arguments can be set using the MORE DATA input section of the SCALE-4 input. About the actual arguments as used in SCALE: NCTP: lattice type to be calculated. All infinite lattices (except SYMMSLABCELL and ASYMSLABCELL) can be used with the present version of DANCOFF-MC (see CSAS4 documentation). The lattice type is determined from the CSAS4 input. If another lattice is specified, DANCOFF-MC will print a warning and will try to use the build in Dancoff procedure. ENVIR: the radius of environment to be taken into account [cm]. The default value is 3.0 cm. This can be set to an other value in MORE DATA as: ENV=new value. IGP: to take into account a gap. The value is determined from the CSAS4 input. ICL: to take into account clad. The value is determined from the CSAS4 input. PITCH: pitch of the lattice [cm]. The value is determined from the CSAS4 input. FUELOD: outside diameter of fuel [cm]. The value is determined from the CSAS4 input. TKMOD2: thickness of the second moderator [cm]. The value is determined from the CSAS4 input. CLADOD: outside diameter of the outer clad [cm]. The value is determined from the CSAS4 input.

20

CLADID: inside diameter of clad [cm]. The value is determined from the CSAS4 input. STCLU: total macroscopic neutron cross section of the clad [cm-1]. The value is determined from the CSAS4 input. STMD: total macroscopic neutron cross section of the outer moderator [cm-1]. The value is determined from the CSAS4 input. STMDIU: total macroscopic neutron cross section of the second (inner) moderator [cm-1]. The value is determined from the CSAS4 input. NCYCLE: number of the Monte Carlo cycles of the calculation. The default value is 1000000. Set to another value in MORE DATA as: NCY=new value. SACCUU: accuracy to be sufficient for the value of Dancoff factor calculated. The default value is 0.0001. Set to another value in more date as: SAC=new value. The Monte Carlo calculation stops when either the cycle number or accuracy is reached. DANFU: the calculated Dancoff factor (output). IER: error parameter (output). The use of Dancoff-MC in SCALE can be activated by using DMC=1 in the MORE DATA input section of CSAS4.

21

Figure 1. Three-dimensional view of the geometry of the two-rod basic algorithm (two parallel cylinders without clad and gap). A is the point of emission of neutron from the surface of rod; x-y is a plane, perpendicular to the rods, containing A. O1 and O2 are the cross points of rod axes with the plane x-y. n is the normal to surface at the point A; axes yω and zω are perpendicular to n and they form, together with n, the frame of reference in which neutron flight direction ΩΩΩΩ is randomly selected according to cosine-current. ΩΩΩΩ xy is the projection of ΩΩΩΩ onto the plane x-y. B* is the point where the neutron enters the target rod, while B is its projection onto the plane x-y. lM is the length run by the neutron in moderator, lxy is the projection of this length onto the plane x-y. C is a point on straight line defined by AB, closest to the axis of target rod. Notation used here corresponds to notation of Fig. 2, 3, and 4.

23

Figure 3. Geometry of the algorithm used to select neutron flight direction in cylindrical arrangements. The two parameters drawn independently to select a flight direction are: APx ( = xΩ ), the normal-to-surface component of the flight direction, and β, which is drawn uniformly from [0 ; 2π) to determine the second (and indirectly third) component of the flight direction in the frame of reference xω-yω-zω (see flow chart in Fig. 4). Notation used here corresponds to notation of Figs. 1, 2 and 4.

24

Figure 4. Flow chart of the two-rod basic algorithm. R1 , R2 and R3 refer to indepen-dent selections from random numbers uniformly distributed in [0 ; 1). Notation used here is the same as in Fig. 1, 2, and 3. (Steps 1 through 3: Select the emission point uniformly at the circumference of cross section circle of emitting rod. Steps 4 through 5: Select the normal-to-surface component of flight direction (along xω). Steps 6 through 9: Select the second (and indirectly third) component of flight direction (in the frame of reference xω-yω-zω). Steps 10 through 12: Investigate whether the flight path approaches the target rod. Steps 13 through 14: Calculate t, the minimal distance from the flight path to the target rod axis. Step 15: Investigates whether the flight path crosses the target rod. Steps 16 through 18: Calculate lxy , the x-y projection of the length run by the neutron in moderator. Step 19: Transforms lxy back to three dimensions. Step 20 or 21: Calculates the Dancoff probability for the investigated flight path.)

27

Figure 7. Flow chart of the two-sphere basic algorithm. R1 , R2 , R3 and R4 refer to independent selections from random numbers uniformly distributed in [0 ; 1). Notation used here is the same as in Fig. 6. (Steps 1 through 7: Select the emission point uniformly at the surface of emitting sphere. Steps 8 through 9: Select the normal-to-surface component of flight direction (along xω). Steps 10 through 12: Select the second (and indirectly third) component of flight direction (in the frame of reference xω-yω-zω). Steps 13 through 14: Transform flight direction into the frame of reference x-y-z. Steps 15 through 17: Investigate whether the flight path approaches the target sphere. Steps 18 through 19: Calculate t, the minimal distance from the flight path to the target sphere centre. Step 20: Investigates whether the flight path crosses the target sphere. Steps 21: Calculates lM , the length run by the neutron in moderator. Step 22 or 23: Calculates the Dancoff probability for the investigated flight path.)

28

Figure 8. Neutron flight path in a general arrangement of fuel rods or spheres containing ‘black’ fuel. (This example illustrates that a straight flight path may cross many clads and gaps before entering the first fuel region, and therefore all these crosses have to be found, and the path lengths in the clads and gaps have to be evaluated, as well, even in the case of ‘black’ fuel.)

29

Symbols of segments as used in the Eq. (2): BC = l C,0 CD = l M,1 DE = l C,1 / 2 FG = l C,1 / 2 GH = l M,2 HI = l C,2 / 2 JK = l F,2 KL = l C,2 / 2 MN = l M,3 NO = l C,3 OP = l M,4 PQ = l C,4 / 2 RS = l F,4 TU = l C,4 /2 Figure 9. Neutron flight path in a general arrangement of fuel rods or spheres containing ‘grey’, i.e., partially transparent fuel. This example illustrates the notation used in Eq. (2), as well.

30

Figure 10. Cross section of the CANDU PHWR 37-element fuel bundle. A, B, C, D, and E mark symmetrically different rod positions.

31

Figure 11. Cross section of a general annular fuel rod or pellet. (This figure is to illustrate the input parameters required by the subroutine DCMC in the case of IANNUL = 1.)

32

Figure 12. Cubic array of spherical fuel pellets (ILATTI = 3). (Most tight case.)

33

Figure 13. Rhombohedral (or dodecahedral or hexagonal close-packed) array of spherical fuel pellets (ILATTI = 4). (Most tight case.)

34

Figure 14. Orthorombic (or column hexagonal) array of spherical fuel pellets (ILATTI = 5). (Most tight case.)

35

Figure 15. An illustration of the DCMCI input parameter, ENVIR, in a square lattice of fuel rods (ILATTI = 1).

36

Figure 16. An illustration of the DCMCI input parameter, ENVIR, in a triangular (hexagonal) lattice of fuel rods (ILATTI = 2).

37

Table 1. Input/output description of the subroutine DCMC 1. Subroutine name: DCMC 2. Purpose: Calculates, by Monte Carlo method, the Dancoff factors

(C) for cylindrical fuel rods or spherical fuel pellets arranged in almost arbitrary geometry. (The only restrictions on the geometry: (1) fuel rods and pellets cannot be mixed in the same arrangement, (2) the cylinders’ axes must be parallelly positioned in rod arrangements.)

3. Usage: CALL DCMC (IGEO, IANNUL, NLUM, XCENT,

YCENT, ZCENT, IGREY, IGP, ICL, RFL, RGP, RCL, STFL, STCL, STMD, RFLI, RGPI, RCLI, STCLI, STMDI, NDANF, INDANF, ICHK, NCYCLE, SACCU, IRAND, DANF, SDEV, NCEX, IWRK1, IWRK2, IWRK3, WRK1, WRK2, WRK3, WRK4, WRK5, WRK6, WRK7, WRK8, IER, IERVEC)

Specifications of the parameters: INTEGER IGEO, IANNUL, NLUM, IGREY, IGP,

ICL, NDANF, INDANF(NDANF), ICHK, IRAND, NCYCLE, NCEX(NDANF), ISEQU(NLUM), ILUMCV(NLUM), NV(NLUM), IER, IERVEC(3)

REAL XCENT(NLUM), YCENT(NLUM),

ZCENT(NLUM), RFL(NLUM), RGP(NLUM), RCL(NLUM), STFL(NLUM), STCL(NLUM), STMD, RFLI(NLUM), RGPI(NLUM), RCLI(NLUM), STCLI(NLUM), STMDI(NLUM), SACCU(NDANF), DANF(NDANF), SDEV(NDANF), C2FHV(NLUM), C2CHV(NLUM), D2CHV(NLUM), DTV(NLUM), DMV(NLUM), DCV(NLUM), DFV(NLUM), RV(NLUM)

38

Table 1. (continued) 4. Description of the input/output parameters:

Parameter Function/meaning name IGEO Input parameter of problem geometry.

IGEO=1 : infinite, cylindrical fuel rods ('fuel pins'); IGEO=2 : spherical fuel pellets ('fuel spheres').

IANNUL Input parameter of the type of fuel lumps to be calculated.

IANNUL=0 : non-annular cylindrical rods or spherical

pellets; IANNUL=1 : annular cylindrical rods or spherical pellets.

In the case of IGREY=1, IANNUL must be equal to zero.

NLUM Input number of all the lumps (rods or pellets) included in the

calculation (i.e., the number of lumps which are inside the region considered as surroundings).

XCENT Input vector of length NLUM containing the x co-ordinates of

the centres of the lumps [cm]. Rods are assumed to be positioned parallelly with z-axis, thus in the case of rods the vector XCENT has to contain the x co-ordinates of the intersection points of the axes of the rods with the x-y plane.

YCENT Input vector of length NLUM containing the y co-ordinates of the

centres of the lumps [cm]. In the case of rods the vector YCENT has to contain the y co-ordinates of the intersection points of the axes of the rods with the x-y plane. The sequence of values must correspond to the sequence used in the vector XCENT.

ZCENT Input vector of length NLUM containing the z co-ordinates of

centres of the spherical fuel pellets [cm]. In the case of rods the data stored in this vector are indifferent to the calculation. The sequence of values must correspond to the sequence used in the vector XCENT.

39

Table 1. (continued)

IGREY Input parameter:

IGREY=0 : 'grey-effect' is not taken into account (i.e., the

fuel regions of the lumps are totally 'black' for neutrons)

IGREY=1 : 'grey-effect' is calculated (i.e., the neutrons have

chance to cross fuel regions without collision) IGP Input parameter:

IGP=0 : no gaps taken into account; IGP=1 : effect of gaps is calculated.

ICL Input parameter:

ICL=0 : no clads taken into account; ICL=1 : effect of clads is calculated.

RFL Input vector of length NLUM containing the (outside) radii of the

fuel regions [cm]. The sequence of values must correspond to the sequence used in the vector XCENT.

RGP Input vector of length NLUM containing the outside radii of the

(outer) gaps [cm]. The sequence of values must correspond to the sequence used in the vector XCENT. If IGP=0, then the data stored in the RGP are indifferent to the calculation.

RCL Input vector of length NLUM containing the outside radii of the

(outer) clads [cm]. The sequence of values must correspond to the sequence used in the vector XCENT. If ICL=0, then the data stored in the RCL are indifferent to the calculation.

STFL Input vector of length NLUM containing the macroscopic total

neutron cross sections of the fuel regions [cm-1]. The sequence of values must correspond to the sequence used in the vector XCENT. If IGREY=0, then the data stored in the STFL are indifferent to the calculation.

STCL Input vector of length NLUM containing the macroscopic total

neutron cross sections of the (outer) clads [cm-1]. The sequence of values must correspond to the sequence used in the vector

40


XCENT. If ICL=0, then the data stored in the STCL are indifferent to the

calculation. STMD Input parameter containing the macroscopic total neutron cross

section of the (outer) moderator (i.e., the moderator found between the fuel lumps) [cm-1].

RFLI Input vector of length NLUM containing the inside (smaller)

radii of the fuel regions in the case of annular geometry (IANNUL=1) [cm]. In the case of IANNUL=0, the data stored in this vector are indifferent to the calculation. The sequence of values must correspond to the sequence used in the vector XCENT.

RGPI Input vector of length NLUM containing the inside (smaller)

radii of the inner gaps in the case of annular geometry (IANNUL=1) [cm]. In the case of IANNUL=0 or IGP=0, the data stored in this vector are indifferent to the calculation. The sequence of values must correspond to the sequence used in the vector XCENT.

RCLI Input vector of length NLUM containing the inside (smaller)

radii of the inner clads in the case of annular geometry (IANNUL=1) [cm]. In the case of IANNUL=0 or ICL=0, the data stored in this vector are indifferent to the calculation. The sequence of values must correspond to the sequence used in the vector XCENT.

STCLI Input vector of length NLUM containing the macroscopic total

neutron cross sections of the inner clads in the case of annular geometry (IANNUL=1) [cm-1]. In the case of IANNUL=0 or ICL=0, the data stored in this vector are indifferent to the calculation. The sequence of values must correspond to the sequence used in the vector XCENT.

STMDI Input vector of length NLUM containing the macroscopic total

neutron cross sections of the inner moderators (i.e., the moderators found in the holes of the annular rods or in the centres of the annular pellets) in the case of annular geometry (IANNUL=1) [cm-1]. In the case of IANNUL=0, the data stored in this vector are indifferent to the calculation. The sequence of values must correspond to the sequence used in the vector XCENT.

41

NDANF Input number of lumps for which Dancoff factor is to be calculated


INDANF Input vector of length NDANF containing the indices of the

lumps for which Dancoff factor is to be calculated. The indexing of the lumps is the same as in the vector XCENT.

ICHK Input parameter:

ICHK=0 : the subroutine DCMCCK does not check for

overlapping lumps. (If the number of lumps included in the calculation is high, then the check for overlapping lumps may take a long time.)

ICHK=1 : total check of the input by the subroutine

DCMCCK. NCYCLE Input number of the Monte Carlo cycles to be executed. In each

cycle one neutron is emitted from each lumps listed in the INDANF vector (i.e., NDANF neutrons are emitted in each cycle).

Remark on this parameter: running time is proportional to

NCYCLE. The calculation of one Dancoff factor with 100,000 cycles, providing typically a statistical accuracy not worse than 0.001, takes 1 to 3 s on a DEC AXP 5/266 computer and 15 to 40 s on a 133 MHz Pentium PC if the number of surrounding lumps taken into account lies in the range from 100 to 400.

SACCU Input vector of length NDANF containing the 'sufficient

accuracy' limits, i.e., the statistical deviation considered to be sufficiently small for the Dancoff factors. The Monte Carlo calculation stops when either the number of cycles reaches NCYCLE or all the deviations (1 x sigma values) of the Dancoff factors being calculated are already less than the related SACCU values.

IRAND Input parameter:

IRAND=0 : the random number generator is initialised by a

constant to produce the same series of pseudorandom numbers from one execution to the next;

42

IRAND=1 : the random number generator is initialised by the system clock (the start of the generator is randomised).


DANF Output vector of length NDANF containing the Dancoff factors

calculated. The sequence of values corresponds to the sequence given by the vector INDANF.

SDEV Output vector of length NDANF containing the standard

deviations (1 x sigma values) of the Dancoff factors calculated. The sequence of these deviations corresponds to the sequence of Dancoff factors in the vector DANF.

NCEX Output vector of length NDANF containing the number of Monte

Carlo cycles executed for calculation of the related Dancoff factor. The sequence of these numbers corresponds to the sequence of the Dancoff factors in the vector NDANF.

IWRK1 Working area (integer vector) of length NLUM. IWRK2 Working area (integer vector) of length NLUM. IWRK3 Working area (integer vector) of length NLUM. WRK1 Working area (real vector) of length NLUM. WRK2 Working area (real vector) of length NLUM. WRK3 Working area (real vector) of length NLUM. WRK4 Working area (real vector) of length NLUM. WRK5 Working area (real vector) of length NLUM. WRK6 Working area (real vector) of length NLUM. WRK7 Working area (real vector) of length NLUM. WRK8 Working area (real vector) of length NLUM. IER Output parameter (error code):

If IER=0, no error detected.

43

Terminal errors: IER=30 indicates that IGEO is less than 1 or greater

than 2.


IER=31 indicates that the number of lumps (NLUM) is less

than 2. IER=32 indicates that IGREY is less than 0 or greater

than 1. IER=33 indicates that IGP is less than 0 or greater than 1. IER=34 indicates that ICL is less than 0 or greater than 1. IER=35 indicates that some STFL(I), I=1,2,...,NLUM, is

negative or greater than 109 cm-1. The index of the first incorrect STFL element is returned in the IERVEC(1). The total number of incorrect STFL elements is returned in the IERVEC(3).

IER=36 indicates that some STCL(I), I=1,2,...,NLUM, is

negative or greater than 109 cm-1. The index of the first incorrect STCL element is returned in the IERVEC(1). The total number of incorrect STCL elements is returned in the IERVEC(3).

IER=37 indicates that STMD is negative or greater than 109

cm-1. IER=38 indicates that NDANF is less than 1 or greater than

NLUM. IER=39 indicates that some INDANF(I), I=1,2,...,NDANF,

is less than 1 or greater than NLUM. The index of the first incorrect INDANF element is returned in the IERVEC(1). The total number of incorrect INDANF elements is returned in the IERVEC(3).

IER=40 indicates that the NCYCLE is less than 1 or greater

than 109. IER=41 indicates that some lumps are too far (> 1000 cm)

from the origin. The index of the first distant lump

44

is returned in the IERVEC(1). The total number of distant lumps is returned in the IERVEC(3).


IER=42 indicates that some RFL(I), I=1,2,...,NLUM, is less than 10-6 cm or greater than 1000 cm. The index of the first incorrect RFL element is returned in the IERVEC(1). The total number of incorrect RFL elements is returned in the IERVEC(3).

IER=43 indicates that some lumps have negative gap

thickness. The index of the first lump having negative gap thickness is returned in the IERVEC(1). The total number of lumps having negative gap thickness is returned in the IERVEC(3).

IER=44 indicates that some lumps have negative clad

thickness. The index of the first lump having negative clad thickness is returned in the IERVEC(1). The total number of lumps having negative clad thickness is returned in the IERVEC(3).

IER=45 indicates that the calculated distance from one to an

other lump is negative, i.e., there are lumps which overlap each other. The indices of the first overlapping pair of lumps are returned in the IERVEC(1) and IERVEC(2). The total number of pairs overlapping each other is returned in the IERVEC(3).

IER=46 indicates that some SACCU(I), I=1,2,...,NDANF, is

negative or greater than 1. The index of the first incorrect SACCU element is returned in the IERVEC(1). The total number of incorrect SACCU elements is returned in the IERVEC(3).

IER=47 indicates that IRAND is less than 0 or greater

than 1. IER=50 indicates that IANNUL is less than 0 or greater than

1.

45

IER=51 indicates that IANNUL is not equal to zero when

IGREY=1.


IER=52 indicates that some RFLI(I), I=1,2,...,NLUM, is

negative or greater than RFL(I). The index of the first incorrect RFLI element is returned in the IERVEC(1). The total number of incorrect RFLI elements is returned in the IERVEC(3).

IER=53 indicates that some inner clad thickness (RFLI(I)-

RCLI(I) or RGPI(I)-RCLI(I), I=1,2,...,NLUM) is negative. The index of the first incorrect inner clad thickness is returned in the IERVEC(1). The total number of incorrect thickness’ is returned in the IERVEC(3).

IER=54 indicates that some inner gap thickness (RFLI(I)-

RGPI(I), I=1,2,..., NLUM) is negative. The index of the first incorrect inner gap thickness is returned in the IERVEC(1). The total number of incorrect thickness’ is returned in the IERVEC(3).

IER=55 indicates that some STCLI(I), I=1,2,...,NLUM, is

negative or greater than 109 cm-1. The index of the first incorrect STCLI element is returned in the IERVEC(1). The total number of incorrect STCLI elements is returned in the IERVEC(3).

IER=56 indicates that some STMDI(I), I=1,2,...,NLUM, is

negative or greater than 109 cm-1. The index of the first incorrect STMDI element is returned in the IERVEC(1). The total number of incorrect STMDI elements is returned in the IERVEC(3).

IERVEC Output vector of length 3 containing additional information to

the error and warning messages. In the case of IER=35, 36, 39, 41, 42, 43, 44, 46, 52, 53, 54, 55, 56, the IERVEC(1) contains the index of the first problematic lump (see the description of these errors) and the IERVEC(3) contains the total number of problematic lumps. In the case of IER=45, the IERVEC(1) and IERVEC(2) contain the indices of the first overlapping pair of

46

lumps and the IERVEC(3) contains the total number of pairs overlapping each other.

5. Required subroutines: DCMCCK, SORT, RNDIN, RNDINC, RNDS

47

Table 2. Input/output description of the subroutine DCMCCK 1. Subroutine name: DCMCCK 2. Purpose: Checks the input parameters of the subroutine DCMC. 3. Usage: CALL DCMCCK (IGEO, IANNUL, NLUM,

XCENT, YCENT, ZCENT, IGREY, IGP, ICL, RFL, RGP, RCL, STFL, STCL, STMD, RFLI, RGPI, RCLI, STCLI, STMDI, NDANF, INDANF, ICHK, NCYCLE, SACCU, IRAND, IER, IERVEC)

Specifications of the parameters: INTEGER IGEO, IANNUL, NLUM, IGREY, IGP,

ICL, NDANF, INDANF(NDANF), ICHK, IRAND, NCYCLE, IER, IERVEC(3)

REAL XCENT(NLUM), YCENT(NLUM),

ZCENT(NLUM), RFL(NLUM), RGP(NLUM), RCL(NLUM), STFL(NLUM), STCL(NLUM), STMD, RFLI(NLUM), RGPI(NLUM), RCLI(NLUM), STCLI(NLUM), STMDI(NLUM), SACCU(NDANF)

4. Description of the input/output parameters: Description of the input/output parameters is the same as that of the subroutine DCMC. 5. Required subroutines: none

48

Table 3. Input/output description of the subroutine SORT 1. Subroutine name: SORT 2. Purpose: Sorts real numbers in ascending order. 3. Usage: CALL SORT(NN, RV, NV) Specifications of the parameters: INTEGER NN, NV(*) REAL RV(*) 4. Description of the input/output parameters:

Parameter Function/meaning name NN Input number of the elements of the vector RV (i.e., the number

of real numbers to be sorted). RV Input/output vector of length NN containing as input: the real numbers to be sorted, as output: the real numbers sorted in ascending order. NV Input/output vector of length NN containing as input: integer numbers indexing the elements of the

vector RV, as output: the indices of the elements of the vector RV in

an order according to the new order of the sorted real numbers.

5. Required subroutines: none

49

Table 4. Input/output description of the subroutine DCMCI 1. Subroutine name: DCMCI 2. Purpose: Prepares the geometrical, material and other problem

describing data needed by the subroutine DCMC in order to calculate the Dancoff factor for regular (infinite) lattices of cylindrical fuel rods or spherical fuel pellets.

3. Usage: CALL DCMCI (ILATTI, ENVIR, IGREY, IGP, ICL,

RFLU, RGPU, RCLU, PITCH, STFLU, STCLU, STMD, IANNUL, RFLIU, RGPIU, RCLIU, STCLIU, STMDIU, NCYCLE, SACCUU, IRAND, NLUM, DANFU, SDEVU, NCEXU, IER, IERVEC)

Specifications of the parameters: INTEGER ILATTI, IGREY, IGP, ICL, IANNUL,

NCYCLE, IRAND, NLUM, NCEXU, IER, IERVEC(3)

REAL ENVIR, RFLU, RGPU, RCLU, PITCH,

STFLU, STCLU, STMD, RFLIU, RGPIU, RCLIU, STCLIU, STMDIU, SACCUU, DANFU, SDEVU

4. Description of the input/output parameters:

Parameter Function/meaning name ILATTI Input parameter of the type of lattice or array configuration to be

calculated. ILATTI=1 : square lattice of cylindrical fuel rods (SCALE

terminology: 'SQUAREPITCH' and 'ASQUAREPITCH': cylindrical rods in a square pitch);

50


ILATTI=2 : triangular lattice of cylindrical fuel rods

(SCALE terminology: 'TRIANGPITCH' and 'ATRIANGPITCH': cylindrical rods in a triangular pitch);

ILATTI=3 : cubic array of spherical fuel pellets (SCALE

terminology: 'SPHSQUAREP' and 'ASPHSQUAREP': spherical pellets in a cubic lattice);

ILATTI=4 : rhombohedral (or dodecahedral or hexagonal

close-packed) array of spherical fuel pellets (SCALE terminology: 'SPHTRIANGP' and 'ASPHTRIANGP': spherical pellets in a bi-centred or face centred hexagonal close-packed lattice);

ILATTI=5 : orthorhombic (or column hexagonal) array of

spherical fuel pellets (not available in SCALE). ENVIR Input parameter containing the radius of environment to be taken

into account. ENVIR must be given in terms of pitch, i.e., the real radius of environment is ENVIR*PITCH. If the centre of a surrounding lump is inside the environment, whole body of this lump is taken into account, even if a certain part of this lump is outside the environment. Limits for ENVIR: If ILATTI=1 or ILATTI=2, then ENVIR

must be less than or equal to 40. If ILATTI greater than 2, then ENVIR must be less than or equal to 10.

IGREY Input parameter:

IGREY=0 : 'grey-effect' is not taken into account (i.e., the

fuel regions of the lumps are totally 'black' for neutrons);

IGREY=1 : ' grey-effect' is calculated (i.e., the neutrons have

chance to cross fuel regions without collision).

51


IGP Input parameter:


ICL Input parameter: ICL=0 : no clads taken into account; ICL=1 : effect of clads is calculated.

RFLU Input parameter containing the (outside) radius of the fuel region

[cm]. RGPU Input parameter containing the outside radius of the (outer) gap

[cm]. If IGP=0, then the datum stored in the RGPU is indifferent to the calculation.

RCLU Input parameter containing the outside radius of the (outer) clad

[cm]. If ICL=0, then the datum stored in the RCLU is indifferent to the calculation.

PITCH Input parameter containing the pitch of the lattice or array, i.e.,

the centre-to-centre spacing between the lumps [cm]. STFLU Input parameter containing the macroscopic total neutron cross

section of the fuel [cm-1]. If IGREY=0, then the datum stored in the STFLU is indifferent to the calculation.

STCLU Input parameter containing the macroscopic total neutron cross

section of the (outer) clad [cm-1]. If ICL=0, then the datum stored in the STCLU is indifferent to the calculation.

STMD Input parameter containing the macroscopic total neutron cross

section of the (outer) moderator (i.e., the moderator found between the fuel lumps) [cm-1].

IANNUL Input parameter of the type of fuel lumps to be calculated.

IANNUL=0 : non-annular cylindrical rods or spherical

pellets; IANNUL=1 : annular cylindrical rods or spherical pellets.

52

In the case of IGREY=1, IANNUL must be equal to zero. Table 4. (continued)

RFLIU Input parameter containing the inside radius of the fuel region in

the case of IANNUL=1 [cm]. In the case of IANNUL=0, the datum stored in the RFLIU is indifferent to the calculation.

RGPIU Input parameter containing the inside (smaller) radius of the

inner gap in the case of IANNUL=1 [cm]. In the case of IANNUL=0 or IGP=0, the datum stored in the RGPIU is indifferent to the calculation.

RCLIU Input parameter containing the inside (smaller) radius of the

inner clad in the case of IANNUL=1 [cm]. In the case of IANNUL=0 or ICL=0, the datum stored in the RCLIU is indifferent to the calculation.

STCLIU Input parameter containing the macroscopic total neutron cross

section of the inner clad [cm-1]. In the case of IANNUL=0 or ICL=0, the datum stored in the STCLIU is indifferent to the calculation.

STMDIU Input parameter containing the macroscopic total neutron cross

section of the inner moderator (i.e., the moderator found in the holes of the annular rods or in the centres of the annular pellets) in the case of annular geometry (IANNUL=1) [cm-1]. In the case of IANNUL=0, the datum stored in the STMDIU is indifferent to the calculation.

NCYCLE Input number of the Monte Carlo cycles to be executed. SACCUU Input parameter containing the 'sufficient accuracy', i.e., the

statistical deviation considered to be sufficiently small for the Dancoff factor. The Monte Carlo calculation stops when either the number of cycles reaches NCYCLE or the standard deviation (1 x sigma) of the Dancoff factor being calculated is already less than the SACCUU value.

IRAND Input parameter:

IRAND=0 : the random number generator is initialised by a

constant to produce the same series of pseudorandom numbers from one execution to the next;

53

IRAND=1 : the random number generator is initialised by the system clock (the start of the generator is randomised).


NLUM Output number of the lumps (rods or pellets) which were

included in the calculation (the number of surrounding lumps plus the source lump together).

DANFU Output parameter containing the Dancoff factor calculated. SDEVU Output parameter containing the standard deviation (1 x sigma)

of the Dancoff factor calculated. NCEXU Output number of the Monte Carlo cycles executed. IER Output parameter (error code).

If IER=0, no error detected.

Error messages generated by this subroutine:

IER=20 indicates that ILATTI is less than 1 or greater

than 5. IER=21 indicates that ENVIR is less than 1, or greater than

40 in the case of ILATTI=1 or ILATTI=2, or greater than 10 in the case of ILATTI greater than 2.

IER=22 indicates that the pitch is negative or equal to zero. IER=23 indicates that IANNUL is less than 0 or greater than

1. IER=24 indicates that IANNUL is not equal to zero when

IGREY=1. IER=25 indicates that the (outside) radius of the fuel region

is greater than half of the pitch; or the (outside) radius of the fuel region is not positive.

IER=26 indicates that the inside radius of the fuel region is

greater than its outside radius; or the inside radius of the fuel region is negative.

54

IER=27 indicates that the (outside) radius of the (outer) clad is less than the (outside) radius of the fuel region; or the (outside) radius of the (outer) clad is greater than half of the pitch.


IER=28 indicates that the inside (smaller) radius of the inner

clad is greater than the inside radius of the fuel region; or the inside (smaller) radius of the inner clad is negative.

IER=29 indicates that the (outside) radius of the (outer) gap

is less than the (outside) radius of the fuel region; or the (outside) radius of the (outer) gap is greater than the (outside) radius of the (outer) clad.

IER=30 indicates that the inside (smaller) radius of the inner

gap is greater than the inside radius of the fuel region; or the inside (smaller) radius of the inner gap is less than the inside (smaller) radius of the inner clad.

Error messages generated by the subroutine DCMC:

IER=32 indicates that IGREY is less than 0 or greater

than 1. IER=33 indicates that IGP is less than 0 or greater than 1. IER=34 indicates that ICL is less than 0 or greater than 1. IER=35 indicates that STFLU is negative or greater than 109

cm-1. IER=36 indicates that STCLU is negative or greater than 109

cm-1. IER=37 indicates that STMD is negative or greater than 109

cm-1. IER=40 indicates that NCYCLE is less than 1 or greater than

109. IER=42 indicates that RFLU is less than 10-6 cm or greater

than 1000 cm. IER=43 indicates that the gap thickness is negative.

55

IER=44 indicates that the clad thickness is negative.


IER=46 indicates that SACCUU is negative or greater

than 1. IER=47 indicates that IRAND is less than 0 or greater

than 1. IER=55 indicates that STCLIU is negative or greater than

109 cm-1. IER=56 indicates that STMDIU is negative or greater than

109 cm-1.

Information on error codes between 31 and 56 not described here is available in the description of the subroutine DCMC.

IERVEC Output vector of length 3 containing additional information to

the error and warning messages. The detailed information on IERVEC is given in the description of the subroutine DCMC.

5. Required subroutines: DCMC, DCMCCK, SORT, RNDIN, RNDINC, RNDS

56

Table 5. Input/output description of the subroutine DCMCIS 1. Subroutine name: DCMCIS 2. Purpose: An interface between the subroutine DCMCI and the

SCALE system (see Appendix 1). 3. Usage: CALL DCMCIS (NCTP, ENVIR, IGP, ICL, PITCH,

FUELOD, TKMOD2, CLADOD, CLADID, STCLU, STMD, STMDIU, NCYCLE, SACCUU, DANFU, IER)

Specifications of the parameters: INTEGER NCTP, IGP, ICL, NCYCLE, IER REAL ENVIR, PITCH, FUELOD, TKMOD2,

CLADOD, CLADID, STCLU, STMD, STMDIU, SACCUU, DANFU

4. Description of the input/output parameters:

Parameter name Function/meaning NCTP Input parameter of the type of lattice or array configuration to be

calculated. NCTP=1 : 'SQUAREPITCH': cylindrical rods in a square

pitch; NCTP=2 : 'ASQUAREPITCH' or 'ASQP': annular cylindrical

rods in a square pitch; NCTP=3 : 'TRIANGPITCH': cylindrical rods in a triangular

pitch; NCTP=4 : 'ATRIANGPITCH' or 'ATRP': annular cylindrical

rods in a triangular pitch; NCTP=5 : 'SPHSQUAREP': spherical pellets in a cubic

lattice; NCTP=6 : 'ASPHSQUAREP' or 'ASSP': annular spherical

pellets in a cubic lattice;

57


NCTP=7 : 'SPHTRIANGP': spherical pellets in a bi-centred or face centred hexagonal close-packed lattice;

NCTP=8 : 'ASPHTRIANGP' or 'ASTP': annular spherical

pellets in a bi-centred or face centred hexagonal close-packed lattice.

ENVIR Input parameter containing the radius of environment to be taken

into account. ENVIR must be given in terms of pitch, i.e., the real radius of environment is ENVIR*PITCH. Limits for ENVIR: If NCTP is less than or equal to 4, then

ENVIR must be less than or equal to 40. If NCTP is greater than or equal to 5, then ENVIR must be less than or equal to 10.

IGP Input parameter:


ICL Input parameter:

ICL=0 : no clads taken into account; ICL=1 : effect of clads is calculated.

PITCH Input parameter containing the pitch of the lattice or array, i.e.,

the centre-to-centre spacing between the lumps [cm]. FUELOD Input parameter containing the outside diameter of the fuel

region [cm]. TKMOD2 Input parameter containing the thickness of the second

moderator, i.e., the diameter of the inner moderator region [cm]. CLADOD Input parameter containing the outside diameter of the outer clad

[cm]. If ICL=0, then the datum stored in the CLADOD is indifferent to the calculation.

58


CLADID Input parameter containing the inside diameter of the outer clad

[cm]. If IGP=0, then the datum stored in the CLADID is indifferent to the calculation.

STCLU Input parameter containing the macroscopic total neutron cross

section of the clad [cm-1]. If ICL=1, then the inner clad has the same cross section as the outer one. If ICL=0, then the datum stored in the STCLU is indifferent to the calculation.

STMD Input parameter containing the macroscopic total neutron cross

section of the outer moderator (i.e., the moderator found between the fuel lumps) [cm-1].

STMDIU Input parameter containing the macroscopic total neutron cross

section of the second (inner) moderator (i.e., the moderator found in the holes of the annular rods or in the centres of the annular pellets) [cm-1]. In the case of non-annular geometry (NCTP = 1, 3, 5, 7), the datum stored in the STMDIU is indifferent to the calculation.

NCYCLE Input number of the Monte Carlo cycles to be executed. SACCUU Input parameter containing the 'sufficient accuracy', i.e., the

statistical deviation considered to be sufficiently small for the Dancoff factor. The Monte Carlo calculation stops when either the number of cycles reaches NCYCLE or the standard deviation (1 x sigma) of the Dancoff factor being calculated is already less than the SACCUU value.

DANFU Output parameter containing the Dancoff factor calculated. IER Output parameter (error code):

If IER=0, no error detected. If IER greater than 0, an error has been detected, and the calculation of the Dancoff factor was not successful.

Error messages generated by this subroutine:

IER=1 indicates that NCTP (the lattice type parameter) is less than 1 or greater than 8, i.e., this lattice can not be calculated by the Dancoff-MC.

59


Error messages generated by the called subroutines:

Information on error codes from 20 to 60 is available in the description of the subroutine DCMCI (in Table 4).

5. Required subroutines: DCMCI, DCMC, DCMCCK, SORT, RNDIN, RNDINC,

RNDS

60

Table 6. List of components of the code package DANCOFF-MC File name Content Subpackage Function

ASKTIM.FOR FORTRAN subroutine SETTIM (with entry ASKTIM)

DCMCD DEC subroutine to start the CPU time measuring and to ask the CPU time elapsed.

COPYIx.BAT

(COPYID.BAT COPYIL.BAT COPYIR.BAT)

MS-DOS batch file

x = D : DCMCDx = L : DCMCL x = R : DCMCR

Under MS-DOS it merges all the necessary FORTRAN source components together to create the complete source program DCMCIx.

COPYISx.BAT

(COPYISD.BAT COPYISL.BAT COPYISR.BAT)

MS-DOS batch file


Under MS-DOS it merges the subroutine DCMCIS and all the subroutines called by DCMCIS together to create the subroutine package DCMCISPx.F(OR).

COPY37x.BAT

(COPY37D.BAT COPY37L.BAT COPY37R.BAT)

MS-DOS batch file


Under MS-DOS it merges all the necessary FORTRAN components together to create the complete source program DCMC37x.

DCMC.FOR FORTRAN subroutine DCMC

All Nucleus subroutine of the Dancoff-MC method. Calculates, by Monte Carlo method, the Dancoff factors (C) for cylindrical fuel rods or spherical fuel pellets arranged in almost arbitrary geometry. (The only restrictions on the geometry: 1) fuel rods and pellets cannot be mixed in the same arrangement, 2) the cylinders’ axes must be parallelly positioned in rod arrangements.)

DCMCCK.FOR FORTRAN subroutine DCMCCK

All Checks the input parameters of the subroutine DCMC.

61


File name Content Subpackage Function

DCMCI.FOR FORTRAN subroutine DCMCI

All Prepares the geometrical, material and other problem describing data needed by the subroutine DCMC in order to calculate Dancoff factor for regular (infinite) lattices of cylindrical fuel rods or spherical fuel pellets.

DCMCIx.F(OR)

(DCMCID.FOR DCMCIL.FOR DCMCIR.F)

Complete FORTRAN program DCMCIx (as merged together by the COPYIx.BAT


Calculates Dancoff factor for regular (infinite) lattices of cylindrical fuel rods or spherical fuel pellets.

DCMCIMx.F(OR)

(DCMCIMD.FOR DCMCIML.FOR DCMCIMR.F)

main FORTRAN program segment of the complete program DCMCIx


Main program segment of the complete program DCMCIx. Reads the necessary input, calls the subroutine DCMCI, and prints the output.

DCMCIS.FOR FORTRAN subroutine DCMCIS

All An interface between the subroutine DCMCI and the SCALE system (see Appendix 1).

DCMCISPx.F(OR)

(DCMCISPD.FOR DCMCISPL.FOR DCMCISPR.F)

FORTRAN subroutine package DCMCISP


A file containing the subroutine DCMCIS and all the subroutines called by DCMCIS.

62



DCMC37x.F(OR)

(DCMC37D.FOR DCMC37L.FOR DCMC37R.F)

Complete FORTRAN program DCMC37x (as merged together by the COPY37x. BAT)


This program is to illustrate how to use DANCOFF-MC for special (irregular) geometries. It calculates the Dancoff factors for the five, symmetrically different fuel rod positions in the CANDU PHWR 37-element fuel bundle.

DCMC37Mx. F(OR)

(DCMC37MD.FOR DCMC37ML.FOR DCMC37MR.F)

main FORTRAN program segment of the complete program DCMC37x


Sample main program to illustrate the usage of the subroutine DCMC by calculating the Dancoff factors for the five, symmetrically different fuel rod positions in the CANDU PHWR 37 element fuel bundle. (It is the main program segment of the complete program DCMC37L). It reads the necessary input, calls the subroutine DCMC, and prints the output.

F77L3.FIG ASCII file DCMCL Configuration file for the Lahey compiler.

IOFN.FOR FORTRAN subroutine IOFN

DCMCL Reads in and checks the input and output file names for the DCMCIL and DCMC37L programs.

PACKINGx.LST

(PACKINGD.LST PACKINGL.LST PACKINGR.LST)

Package list (ASCII file)


List of files packed into the subpackage DCMCx

63



RNDINx.F(OR)

(RNDIND.FOR RNDINL.FOR RNDINR.F)

FORTRAN subroutine RNDIN


Initialises the random number generator by the system clock.

RNDINCx.F(OR)

(RNDINCD.FOR RNDINCL.FOR RNDINCR.F)

FORTRAN subroutine RNDINC


Initialises the random number generator to produce the same series of pseudorandom number from one execution to the next (routine used for test purposes).

RNDSx.F(OR)

(RNDSD.FOR RNDSL.FOR RNDSR.F)

FORTRAN subroutine RNDS


Indirect calling of random number generator.

SORT.FOR FORTRAN subroutine SORT

All Sorts real numbers in ascending order.

SMPI1.INP Sample input - 1 for the program DCMCIx

All Sample input for the program DCMCIx. (Square lattice of rods.)


All Sample input for the program DCMCIx. (Square lattice of ‘grey’ rods.)


All Sample input for the program DCMCIx. (Hexagonal lattice of annular rods.)

64




All Sample input for the program DCMCIx. (Closed packed lattice of spherical pellets.)

SMPI1x.OUT

(SMPI1D.OUT SMPI1L.OUT SMPI1R.OUT)

Sample output - 1 generated by the program DCMCIx


Output generated by the program DCMCIx using the sample input SMPI1.INP. (Square lattice of rods.)

SMPI2x.OUT




Output generated by the program DCMCIx using the sample input SMPI2.INP. (Square lattice of ‘grey’ rods.)

SMPI3x.OUT




Output generated by the program DCMCIx using the sample input SMPI3.INP. (Hexagonal lattice of annular rods.)

SMPI4x.OUT




Output generated by the program DCMCIx using the sample input SMPI4.INP. (Closed packed lattice of spherical pellets.)

SMP371.INP Sample input - 1 for the program DCMC37x

All Sample input for the program DCMC37x. (Moderator with low sigma-total.)

SMP372.INP Sample input - 2 for the program DCMC37x

All Sample input for the program DCMC37x. (Moderator with high sigma-total.)

65



SMP371x.OUT

(SMP371D.OUT SMP371L.OUT SMP371R.OUT)

Sample output - 1 generated by the program DCMC37x


Output generated by the program DCMC37x using the sample input SMP371.INP. (Moderator with low sigma-total.)

SMP372x.OUT

(SMP372D.OUT SMP372L.OUT SMP372R.OUT)

Sample output - 2 generated by the program DCMC37x


Output generated by the program DCMC37x using the sample input SMP371.INP. (Moderator with high sigma-total.)

66

Table 7. Input of the sample problem 1 for DCMCIx programs. (Square lattice of rods.) Sample problem 1 for DCMCIx (Square lattice of rods)ILATTI Lattice type [squ=1, hex=2, cub=3, rho=4, ort=5] I 1ENVIR Radius of the environment [pitches] F 10.000IGREY Grey effect ? [yes=1, no=0] I 0IGP Is there any gap ? [yes=1, no=0] I 1ICL Is there any clad ? [yes=1, no=0] I 1RFLU Outside radius of the fuel region [cm] F 0.350RGPU Outside radius of the (outer) gap [cm] F 0.400RCLU Outside radius of the (outer) clad [cm] F 0.500PITCH Pitch [cm] F 1.700STFLU Sigma total of the fuel [1/cm] F 0.000STCLU Sigma total of the (outer) clad [1/cm] F 0.192STMD Sigma total of the (outer) moderator [1/cm] F 1.170IANNUL Lump type [non-annular=0, annular=1] I 0RFLIU Inside radius of the fuel region [cm] F 0.000RGPIU Inside (smaller) radius of the inner gap [cm] F 0.000RCLIU Inside (smaller) radius of the inner clad [cm] F 0.000STCLIU Sigma total of the inner clad [1/cm] F 0.000STMDIU Sigma total of the inner moderator [1/cm] F 0.000NCYCLE Number of Monte Carlo cycles to be executed I 10000SACCUU Sufficient accuracy for the Dancoff factor F 0.0001IRAND Randomize the start of the RNG ? [yes=1, no=0] I 0

Table 8. Input of the sample problem 2 for DCMCIx programs. (Square lattice of ‘grey’ rods.) Sample problem 2 for DCMCIx (Square lattice of 'grey' rods)ILATTI Lattice type [squ=1, hex=2, cub=3, rho=4, ort=5] I 1ENVIR Radius of the environment [pitches] F 20.000IGREY Grey effect ? [yes=1, no=0] I 1IGP Is there any gap ? [yes=1, no=0] I 1ICL Is there any clad ? [yes=1, no=0] I 1RFLU Outside radius of the fuel region [cm] F 0.350RGPU Outside radius of the (outer) gap [cm] F 0.400RCLU Outside radius of the (outer) clad [cm] F 0.500PITCH Pitch [cm] F 1.700STFLU Sigma total of the fuel [1/cm] F 5.889STCLU Sigma total of the (outer) clad [1/cm] F 0.192STMD Sigma total of the (outer) moderator [1/cm] F 1.170IANNUL Lump type [non-annular=0, annular=1] I 0RFLIU Inside radius of the fuel region [cm] F 0.000RGPIU Inside (smaller) radius of the inner gap [cm] F 0.000RCLIU Inside (smaller) radius of the inner clad [cm] F 0.000STCLIU Sigma total of the inner clad [1/cm] F 0.000STMDIU Sigma total of the inner moderator [1/cm] F 0.000NCYCLE Number of Monte Carlo cycles to be executed I 10000SACCUU Sufficient accuracy for the Dancoff factor F 0.0001IRAND Randomize the start of the RNG ? [yes=1, no=0] I 0

67

Table 9. Input of the sample problem 3 for DCMCIx programs. (Hexagonal lattice of annular rods.) Sample problem 3 for DCMCIx (Hexagonal lattice of annular rods)ILATTI Lattice type [squ=1, hex=2, cub=3, rho=4, ort=5] I 2ENVIR Radius of the environment [pitches] F 10.000IGREY Grey effect ? [yes=1, no=0] I 0IGP Is there any gap ? [yes=1, no=0] I 1ICL Is there any clad ? [yes=1, no=0] I 1RFLU Outside radius of the fuel region [cm] F 0.350RGPU Outside radius of the (outer) gap [cm] F 0.400RCLU Outside radius of the (outer) clad [cm] F 0.500PITCH Pitch [cm] F 1.500STFLU Sigma total of the fuel [1/cm] F 0.000STCLU Sigma total of the (outer) clad [1/cm] F 0.192STMD Sigma total of the (outer) moderator [1/cm] F 1.170IANNUL Lump type [non-annular=0, annular=1] I 1RFLIU Inside radius of the fuel region [cm] F 0.200RGPIU Inside (smaller) radius of the inner gap [cm] F 0.150RCLIU Inside (smaller) radius of the inner clad [cm] F 0.100STCLIU Sigma total of the inner clad [1/cm] F 0.192STMDIU Sigma total of the inner moderator [1/cm] F 1.170NCYCLE Number of Monte Carlo cycles to be executed I 10000SACCUU Sufficient accuracy for the Dancoff factor F 0.0001IRAND Randomize the start of the RNG ? [yes=1, no=0] I 0

Table 10. Input of the sample problem 3 for DCMCIx programs. (Close packed lattice of spherical pellets.) Sample problem 4 for DCMCIx (Close packed lattice of spherical pellets)ILATTI Lattice type [squ=1, hex=2, cub=3, rho=4, ort=5] I 4ENVIR Radius of the environment [pitches] F 3.000IGREY Grey effect ? [yes=1, no=0] I 0IGP Is there any gap ? [yes=1, no=0] I 1ICL Is there any clad ? [yes=1, no=0] I 1RFLU Outside radius of the fuel region [cm] F 0.400RGPU Outside radius of the (outer) gap [cm] F 0.420RCLU Outside radius of the (outer) clad [cm] F 0.500PITCH Pitch [cm] F 1.000STFLU Sigma total of the fuel [1/cm] F 0.000STCLU Sigma total of the (outer) clad [1/cm] F 0.238STMD Sigma total of the (outer) moderator [1/cm] F 0.896IANNUL Lump type [non-annular=0, annular=1] I 0RFLIU Inside radius of the fuel region [cm] F 0.000RGPIU Inside (smaller) radius of the inner gap [cm] F 0.000RCLIU Inside (smaller) radius of the inner clad [cm] F 0.000STCLIU Sigma total of the inner clad [1/cm] F 0.000STMDIU Sigma total of the inner moderator [1/cm] F 0.000NCYCLE Number of Monte Carlo cycles to be executed I 100000SACCUU Sufficient accuracy for the Dancoff factor F 0.001IRAND Randomize the start of the RNG ? [yes=1, no=0] I 0

68

Table 11. Input of the sample problem 1 for DCMC37x programs. (Moderator with low sigma-total) Sample problem 1 for DCMC37 (Moderator with low sigma total)IGREY Grey effect ? [yes=1, no=0] I 0STFUELU Sigma total of the fuel [1/cm] F 10000.000STCLADU Sigma total of the clad [1/cm] F 1.000STMOD Sigma total of the moderator [1/cm] F 0.500NCYCLE Number of Monte Carlo cycles to be executed I 10000SACCUU Sufficient accuracy for the Dancoff factors F 0.003IRAND Randomize the start of the RNG ? [yes=1, no=0] I 0

Table 12. Input of the sample problem 2 for DCMC37x programs. (Moderator with high sigma-total) Sample problem 2 for DCMC37 (Moderator with high sigma total)IGREY Grey effect ? [yes=1, no=0] I 0STFUELU Sigma total of the fuel [1/cm] F 10000.000STCLADU Sigma total of the clad [1/cm] F 1.000STMOD Sigma total of the moderator [1/cm] F 1.500NCYCLE Number of Monte Carlo cycles to be executed I 10000SACCUU Sufficient accuracy for the Dancoff factors F 0.003IRAND Randomize the start of the RNG ? [yes=1, no=0] I 0

69

Table 13. Output of the sample problem 1 generated by DCMCID program. (Square lattice of rods.) Sample problem 1 for DCMCIx (Square lattice of rods)

Input values

ILATTI Lattice type [squ=1,hex=2,ssq=3,rho=4,ort=5] : 1ENVIR Radius of the environment [pitches] : 10.00000IGREY Grey effect ? [yes=1, no=0] : 0IGP Is there any gap ? [yes=1, no=0] : 1ICL Is there any clad ? [yes=1, no=0] : 1RFLU Outside radius of the fuel region [cm] : 0.35000RGPU Outside radius of the (outer) gap [cm] : 0.40000RCLU Outside radius of the (outer) clad [cm] : 0.50000PITCH Pitch [cm] : 1.70000STFLU Sigma total of the fuel [1/cm] : 0.00000STCLU Sigma total of the (outer) clad [1/cm] : 0.19200STMD Sigma total of the (outer) moderator [1/cm] : 1.17000IANNUL Lump type [non-annular=0, annular=1] : 0RFLIU Inside radius of the fuel region [cm] : 0.00000RGPIU Inside (smaller) radius of the inner gap [cm] : 0.00000RCLIU Inside (smaller) radius of the inner clad [cm] : 0.00000STCLIU Sigma total of the inner clad [1/cm] : 0.00000STMDIU Sigma total of the inner moderator [1/cm] : 0.00000NCYCLE Number of Monte Carlo cycles to be executed : 10000SACCUU Sufficient accuracy for the Dancoff factor : 0.00010IRAND Randomize the start of the RNG ? [yes=1, no=0] : 0

Results

NLUM Number of lumps taken into account : 317DANFU Dancoff factor calculated : 0.11627SDEVU Standard deviation of the Dancoff factor : 0.00143NCEXU Number of cycles executed : 10000

CPU time used: 0.22 seconds.

70

Table 14. Output of the sample problem 1 generated by DCMCIL program. (Square lattice of rods.) Sample problem 1 for DCMCIx (Square lattice of rods)

Input values

ILATTI Lattice type [squ=1,hex=2,cub=3,rho=4,ort=5] : 1ENVIR Radius of the environment [pitches] : 10.00000IGREY Grey effect ? [yes=1, no=0] : 0IGP Is there any gap ? [yes=1, no=0] : 1ICL Is there any clad ? [yes=1, no=0] : 1RFLU Outside radius of the fuel region [cm] : 0.35000RGPU Outside radius of the (outer) gap [cm] : 0.40000RCLU Outside radius of the (outer) clad [cm] : 0.50000PITCH Pitch [cm] : 1.70000STFLU Sigma total of the fuel [1/cm] : 0.00000STCLU Sigma total of the (outer) clad [1/cm] : 0.19200STMD Sigma total of the (outer) moderator [1/cm] : 1.17000IANNUL Lump type [non-annular=0, annular=1] : 0RFLIU Inside radius of the fuel region [cm] : 0.00000RGPIU Inside (smaller) radius of the inner gap [cm] : 0.00000RCLIU Inside (smaller) radius of the inner clad [cm] : 0.00000STCLIU Sigma total of the inner clad [1/cm] : 0.00000STMDIU Sigma total of the inner moderator [1/cm] : 0.00000NCYCLE Number of Monte Carlo cycles to be executed : 10000SACCUU Sufficient accuracy for the Dancoff factor : 0.00010IRAND Randomize the start of the RNG ? [yes=1, no=0] : 0

Results


71

Table 15. Output of the sample problem 1 generated by DCMCIR program. (Square lattice of rods.) Sample problem 1 for DCMCIx (Square lattice of rods)

Input values

ILATTI Lattice type [squ=1,hex=2,ssq=3,rho=4,ort=5] : 1ENVIR Radius of the environment [pitches] : 10.00000IGREY Grey effect ? [yes=1, no=0] : 0IGP Is there any gap ? [yes=1, no=0] : 1ICL Is there any clad ? [yes=1, no=0] : 1RFLU Outside radius of the fuel region [cm] : .35000RGPU Outside radius of the (outer) gap [cm] : .40000RCLU Outside radius of the (outer) clad [cm] : .50000PITCH Pitch [cm] : 1.70000STFLU Sigma total of the fuel [cm-1] : .00000STCLU Sigma total of the (outer) clad [cm-1] : .19200STMD Sigma total of the (outer) moderator [cm-1] : 1.17000IANNUL Lump type [non-annular=0, annular=1] : 0RFLIU Inside radius of the fuel region [cm] : .00000RGPIU Inside (smaller) radius of the inner gap [cm] : .00000RCLIU Inside (smaller) radius of the inner clad [cm] : .00000STCLIU Sigma total of the inner clad [cm-1] : .00000STMDIU Sigma total of the inner moderator [cm-1] : .00000NCYCLE Number of Monte Carlo cycles to be executed : 10000SACCUU Sufficient accuracy for the Dancoff factor : .00010IRAND Randomize the start of the RNG ? [yes=1, no=0] : 0

Results

NLUM Number of lumps taken into account : 317DANFU Dancoff factor calculated : .11542SDEVU Standard deviation of the Dancoff factor : .00142NCEXU Number of cycles executed : 10000

72

Table 16. Output of the sample problem 2 generated by DCMCID program. (Square lattice of ‘grey’ rods.) Sample problem 2 for DCMCIx (Square lattice of 'grey' rods)

Input values


Results



73

Table 17. Output of the sample problem 2 generated by DCMCIL program. (Square lattice of ‘grey’ rods.) Sample problem 2 for DCMCIx (Square lattice of 'grey' rods)

Input values


Results


74

Table 18. Output of the sample problem 2 generated by DCMCIR program. (Square lattice of ‘grey’ rods.) Sample problem 2 for DCMCIx (Square lattice of 'grey' rods)

Input values

ILATTI Lattice type [squ=1,hex=2,ssq=3,rho=4,ort=5] : 1ENVIR Radius of the environment [pitches] : 20.00000IGREY Grey effect ? [yes=1, no=0] : 1IGP Is there any gap ? [yes=1, no=0] : 1ICL Is there any clad ? [yes=1, no=0] : 1RFLU Outside radius of the fuel region [cm] : .35000RGPU Outside radius of the (outer) gap [cm] : .40000RCLU Outside radius of the (outer) clad [cm] : .50000PITCH Pitch [cm] : 1.70000STFLU Sigma total of the fuel [cm-1] : 5.88900STCLU Sigma total of the (outer) clad [cm-1] : .19200STMD Sigma total of the (outer) moderator [cm-1] : 1.17000IANNUL Lump type [non-annular=0, annular=1] : 0RFLIU Inside radius of the fuel region [cm] : .00000RGPIU Inside (smaller) radius of the inner gap [cm] : .00000RCLIU Inside (smaller) radius of the inner clad [cm] : .00000STCLIU Sigma total of the inner clad [cm-1] : .00000STMDIU Sigma total of the inner moderator [cm-1] : .00000NCYCLE Number of Monte Carlo cycles to be executed : 10000SACCUU Sufficient accuracy for the Dancoff factor : .00010IRAND Randomize the start of the RNG ? [yes=1, no=0] : 0

Results


75

Table 19. Output of the sample problem 3 generated by DCMCID program. (Hexagonal lattice of annular rods.) Sample problem 3 for DCMCIx (Hexagonal lattice of annular rods)

Input values


Results



76

Table 20. Output of the sample problem 3 generated by DCMCIL program. (Hexagonal lattice of annular rods.) Sample problem 3 for DCMCIx (Hexagonal lattice of annular rods)

Input values


Results


77

Table 21. Output of the sample problem 3 generated by DCMCIR program. (Hexagonal lattice of annular rods.) Sample problem 3 for DCMCIx (Hexagonal lattice of annular rods)

Input values

ILATTI Lattice type [squ=1,hex=2,ssq=3,rho=4,ort=5] : 2ENVIR Radius of the environment [pitches] : 10.00000IGREY Grey effect ? [yes=1, no=0] : 0IGP Is there any gap ? [yes=1, no=0] : 1ICL Is there any clad ? [yes=1, no=0] : 1RFLU Outside radius of the fuel region [cm] : .35000RGPU Outside radius of the (outer) gap [cm] : .40000RCLU Outside radius of the (outer) clad [cm] : .50000PITCH Pitch [cm] : 1.50000STFLU Sigma total of the fuel [cm-1] : .00000STCLU Sigma total of the (outer) clad [cm-1] : .19200STMD Sigma total of the (outer) moderator [cm-1] : 1.17000IANNUL Lump type [non-annular=0, annular=1] : 1RFLIU Inside radius of the fuel region [cm] : .20000RGPIU Inside (smaller) radius of the inner gap [cm] : .15000RCLIU Inside (smaller) radius of the inner clad [cm] : .10000STCLIU Sigma total of the inner clad [cm-1] : .19200STMDIU Sigma total of the inner moderator [cm-1] : 1.17000NCYCLE Number of Monte Carlo cycles to be executed : 10000SACCUU Sufficient accuracy for the Dancoff factor : .00010IRAND Randomize the start of the RNG ? [yes=1, no=0] : 0

Results


78

Table 22. Output of the sample problem 4 generated by DCMCID program. (Close packed lattice of spherical pellets.) Sample problem 4 for DCMCIx (Close packed lattice of spherical pellets)

Input values


Results



79

Table 23. Output of the sample problem 4 generated by DCMCIL program. (Close packed lattice of spherical pellets.) Sample problem 4 for DCMCIx (Close packed lattice of spherical pellets)

Input values


Results


80

Table 24. Output of the sample problem 4 generated by DCMCIR program. (Close packed lattice of spherical pellets.) Sample problem 4 for DCMCIx (Close packed lattice of spherical pellets)

Input values

ILATTI Lattice type [squ=1,hex=2,ssq=3,rho=4,ort=5] : 4ENVIR Radius of the environment [pitches] : 3.00000IGREY Grey effect ? [yes=1, no=0] : 0IGP Is there any gap ? [yes=1, no=0] : 1ICL Is there any clad ? [yes=1, no=0] : 1RFLU Outside radius of the fuel region [cm] : .40000RGPU Outside radius of the (outer) gap [cm] : .42000RCLU Outside radius of the (outer) clad [cm] : .50000PITCH Pitch [cm] : 1.00000STFLU Sigma total of the fuel [cm-1] : .00000STCLU Sigma total of the (outer) clad [cm-1] : .23800STMD Sigma total of the (outer) moderator [cm-1] : .89600IANNUL Lump type [non-annular=0, annular=1] : 0RFLIU Inside radius of the fuel region [cm] : .00000RGPIU Inside (smaller) radius of the inner gap [cm] : .00000RCLIU Inside (smaller) radius of the inner clad [cm] : .00000STCLIU Sigma total of the inner clad [cm-1] : .00000STMDIU Sigma total of the inner moderator [cm-1] : .00000NCYCLE Number of Monte Carlo cycles to be executed : 100000SACCUU Sufficient accuracy for the Dancoff factor : .00100IRAND Randomize the start of the RNG ? [yes=1, no=0] : 0

Results


81

Table 25. Output of the sample problem 1 generated by DCMC37D program. (Moderator with low sigma total.) Sample problem 1 for DCMC37 (Moderator with low sigma total)

Input values

IGREY Grey effect ? [yes=1, no=0] : 0STFUELU Sigma total of the fuel [1/cm] :10000.00000STCLADU Sigma total of the clad [1/cm] : 1.00000STMOD Sigma total of the moderator [1/cm] : 0.50000NCYCLE Number of Monte Carlo cycles to be executed : 10000SACCUU Sufficient accuracy for the Dancoff factors : 0.00300IRAND Randomize the start of the RNG ? [yes=1, no=0] : 0

Results

DANF SDEV NCEXDancoff factor Standard deviation Number of cycles

calculated of the Dancoff factor executed

0.62400 0.00300 50000.61297 0.00289 40000.58373 0.00297 50000.35704 0.00334 100000.34932 0.00329 10000


Table 26. Output of the sample problem 1 generated by DCMC37L program. (Moderator with low sigma total.) Sample problem 1 for DCMC37 (Moderator with low sigma total)

Input values

IGREY Grey effect ? [yes=1, no=0] : 0STFUELU Sigma total of the fuel [1/cm] : 10000.00000STCLADU Sigma total of the clad [1/cm] : 1.00000STMOD Sigma total of the moderator [1/cm] : 0.50000NCYCLE Number of Monte Carlo cycles to be executed : 10000SACCUU Sufficient accuracy for the Dancoff factors : 0.00300IRAND Randomize the start of the RNG ? [yes=1, no=0] : 0

Results



0.62873 0.00298 50000.62017 0.00289 40000.58364 0.00295 50000.35408 0.00333 100000.34556 0.00329 10000

82

Table 27. Output of the sample problem 1 generated by DCMC37R program. (Moderator with low sigma total.) Sample problem 1 for DCMC37 (Moderator with low sigma total)

Input values

IGREY Grey effect ? [yes=1, no=0] : 0STFUELU Sigma total of the fuel [1/cm] : 10000.00000STCLADU Sigma total of the clad [1/cm] : 1.00000STMOD Sigma total of the moderator [1/cm] : .50000NCYCLE Number of Monte Carlo cycles to be executed : 10000SACCUU Sufficient accuracy for the Dancoff factors : .00300IRAND Randomize the start of the RNG ? [yes=1, no=0] : 0

Results



.62575 .00296 5000

.61240 .00292 4000

.58035 .00297 5000

.35782 .00335 10000

.35539 .00329 10000

Table 28. Output of the sample problem 2 generated by DCMC37D program. (Moderator with high sigma total.) Sample problem 2 for DCMC37 (Moderator with high sigma total)

Input values

IGREY Grey effect ? [yes=1, no=0] : 0STFUELU Sigma total of the fuel [1/cm] :10000.00000STCLADU Sigma total of the clad [1/cm] : 1.00000STMOD Sigma total of the moderator [1/cm] : 1.50000NCYCLE Number of Monte Carlo cycles to be executed : 10000SACCUU Sufficient accuracy for the Dancoff factors : 0.00300IRAND Randomize the start of the RNG ? [yes=1, no=0] : 0

Results



0.42126 0.00276 60000.38505 0.00297 50000.34942 0.00275 60000.22233 0.00294 70000.21084 0.00295 6000


83

Table 29. Output of the sample problem 2 generated by DCMC37L program. (Moderator with high sigma total.) Sample problem 2 for DCMC37 (Moderator with high sigma total)

Input values

IGREY Grey effect ? [yes=1, no=0] : 0STFUELU Sigma total of the fuel [1/cm] : 10000.00000STCLADU Sigma total of the clad [1/cm] : 1.00000STMOD Sigma total of the moderator [1/cm] : 1.50000NCYCLE Number of Monte Carlo cycles to be executed : 10000SACCUU Sufficient accuracy for the Dancoff factors : 0.00300IRAND Randomize the start of the RNG ? [yes=1, no=0] : 0

Results



0.42561 0.00275 60000.39035 0.00274 60000.35105 0.00276 60000.22113 0.00295 70000.20575 0.00294 6000

Table 30. Output of the sample problem 2 generated by DCMC37R program. (Moderator with high sigma total.) Sample problem 2 for DCMC37 (Moderator with high sigma total)

Input values

IGREY Grey effect ? [yes=1, no=0] : 0STFUELU Sigma total of the fuel [1/cm] : 10000.00000STCLADU Sigma total of the clad [1/cm] : 1.00000STMOD Sigma total of the moderator [1/cm] : 1.50000NCYCLE Number of Monte Carlo cycles to be executed : 10000SACCUU Sufficient accuracy for the Dancoff factors : .00300IRAND Randomize the start of the RNG ? [yes=1, no=0] : 0

Results



.41989 .00277 6000

.38351 .00299 5000

.34943 .00276 6000

.22445 .00297 7000

.21317 .00295 6000

84

Table 31. List of files packed in the program subpackage DCMCD (DANCOFF-MC DEC AXP version) File description File name PACKAGE INFORMATION Packing list PACKINGD.LST PROGRAMS Complete program DCMCID (as merged together by the COPYID.BAT) DCMCID.FOR Complete program DCMC37D (as merged together by the COPY37D.BAT) DCMC37D.FOR

MAIN SEGMENTS Main program segment of the complete program DCMCID DCMCIMD.FOR Main program segment of the complete program DCMC37D DCMC37MD.FOR

SUBROUTINES Subroutine to calculate regular (infinite) lattices DCMCI.FOR Nucleus subroutine of the Dancoff-MC method DCMC.FOR Subroutine to check the input parameters of the subroutine DCMC DCMCCK.FOR Subroutine to sort real numbers in ascending order SORT.FOR Subroutine to initialise the random number generator by the system clock RNDIND.FOR Subroutine to initialise the random number generator by a constant RNDINCD.FOR Subroutine to call the random number generator indirectly RNDSD.FOR DEC specific subroutine for CPU time measuring ASKTIM.FOR Subroutine to make the subroutine DCMCI callable from the SCALE system (interface between DCMCI and SCALE) DCMCIS.FOR Subroutine package DCMCISPD (i.e. a FORTRAN file containing the subroutine DCMCIS and all the subroutines called by DCMCIS) DCMCISPD.FOR

SAMPLE INPUTS Sample input /1 for the program DCMCID SMPI1.INP Sample input /2 for the program DCMCID SMPI2.INP Sample input /3 for the program DCMCID SMPI3.INP Sample input /4 for the program DCMCID SMPI4.INP Sample input /1 for the program DCMC37D SMP371.INP Sample input /2 for the program DCMC37D SMP372.INP

85

Table 31. (continued) File description File name SAMPLE OUTPUTS Output generated by the program DCMCID using the sample input SMPI1.INP SMPI1D.OUT Output generated by the program DCMCID using the sample input SMPI2.INP SMPI2D.OUT Output generated by the program DCMCID using the sample input SMPI3.INP SMPI3D.OUT Output generated by the program DCMCID using the sample input SMPI4.INP SMPI4D.OUT Output generated by the program DCMC37D using the sample input SMP371.INP SMP371D.OUT Output generated by the program DCMC37D using the sample input SMP372.INP SMP372D.OUT

MISCELLANEOUS MS-DOS batch file to merge the FORTRAN components together to create the complete program DCMCID COPYID.BAT MS-DOS batch file to merge the FORTRAN components together to create the subroutine package DCMCISPD COPYISD.BAT MS-DOS batch file to merge the FORTRAN components together to create the complete program DCMC37D COPY37D.BAT

86

Table 32. List of files packed in the program subpackage DCMCL (DANCOFF-MC PC / Lahey version) File description File name PACKAGE INFORMATION Packing list PACKINGL.LST PROGRAMS Complete program DCMCIL (as merged together by the COPYIL.BAT) DCMCIL.FOR Complete program DCMC37L (as merged together by the COPY37L.BAT) DCMC37L.FOR

MAIN SEGMENTS Main program segment of the complete program DCMCIL DCMCIML.FOR Main program segment of the complete program DCMC37L DCMC37ML.FOR

SUBROUTINES Subroutine to check the input/output file names IOFN.FOR Subroutine to calculate regular (infinite) lattices DCMCI.FOR Nucleus subroutine of the Dancoff-MC method DCMC.FOR Subroutine to check the input parameters of the subroutine DCMC DCMCCK.FOR Subroutine to sort real numbers in ascending order SORT.FOR Subroutine to initialise the random number generator by the system clock RNDINL.FOR Subroutine to initialise the random number generator by a constant RNDINCL.FOR Subroutine to call the random number generator indirectly RNDSL.FOR Subroutine to make the subroutine DCMCI callable from the SCALE system (interface between DCMCI and SCALE) DCMCIS.FOR Subroutine package DCMCISPL (i.e. a FORTRAN file containing the subroutine DCMCIS and all the subroutines called by DCMCIS) DCMCISPL.FOR

SAMPLE INPUTS Sample input /1 for the program DCMCIL SMPI1.INP Sample input /2 for the program DCMCIL SMPI2.INP Sample input /3 for the program DCMCIL SMPI3.INP Sample input /4 for the program DCMCIL SMPI4.INP Sample input /1 for the program DCMC37L SMP371.INP Sample input /2 for the program DCMC37L SMP372.INP

87

Table 32. (continued) File description File name SAMPLE OUTPUTS Output generated by the program DCMCIL using the sample input SMPI1.INP SMPI1L.OUT Output generated by the program DCMCIL using the sample input SMPI2.INP SMPI2L.OUT Output generated by the program DCMCIL using the sample input SMPI3.INP SMPI3L.OUT Output generated by the program DCMCIL using the sample input SMPI4.INP SMPI4L.OUT Output generated by the program DCMC37L using the sample input SMP371.INP SMP371L.OUT Output generated by the program DCMC37L using the sample input SMP372.INP SMP372L.OUT

MISCELLANEOUS MS-DOS batch file to merge the FORTRAN components together to create the complete program DCMCIL COPYIL.BAT MS-DOS batch file to merge the FORTRAN components together to create the subroutine package DCMCISPL COPYISL.BAT MS-DOS batch file to merge the FORTRAN components together to create the complete program DCMC37L COPY37L.BAT Configuration file for Lahey compiler F77L3.FIG

88

Table 33. List of files packed in the program subpackage DCMCR (DANCOFF-MC IBM RISC version) File description File name PACKAGE INFORMATION Packing list PACKINGR.LST PROGRAMS Complete program DCMCIR (as merged together by the COPYIR.BAT) DCMCIR.F Complete program DCMC37R (as merged together by the COPY37R.BAT) DCMC37R.F

MAIN SEGMENTS Main program segment of the complete program DCMCIR DCMCIMR.F Main program segment of the complete program DCMC37R DCMC37MR.F

SUBROUTINES Subroutine to calculate regular (infinite) lattices DCMCI.FOR Nucleus subroutine of the Dancoff-MC method DCMC.FOR Subroutine to check the input parameters of the subroutine DCMC DCMCCK.FOR Subroutine to sort real numbers in ascending order SORT.FOR Subroutine to initialise the random number generator by the system clock RNDINR.F Subroutine to initialise the random number generator by a constant RNDINCR.F Subroutine to call the random number generator indirectly RNDSR.F Subroutine to make the subroutine DCMCI callable from the SCALE system (interface between DCMCI and SCALE) DCMCIS.FOR Subroutine package DCMCISPR (i.e. a FORTRAN file containing the subroutine DCMCIS and all the subroutines called by DCMCIS) DCMCISPR.F

SAMPLE INPUTS Sample input /1 for the program DCMCIR SMPI1.INP Sample input /2 for the program DCMCIR SMPI2.INP Sample input /3 for the program DCMCIR SMPI3.INP Sample input /4 for the program DCMCIR SMPI4.INP Sample input /1 for the program DCMC37R SMP371.INP Sample input /2 for the program DCMC37R SMP372.INP

89

Table 33. (continued) File description File name SAMPLE OUTPUTS Output generated by the program DCMCIR using the sample input SMPI1.INP SMPI1R.OUT Output generated by the program DCMCIR using the sample input SMPI2.INP SMPI2R.OUT Output generated by the program DCMCIR using the sample input SMPI3.INP SMPI3R.OUT Output generated by the program DCMCIR using the sample input SMPI4.INP SMPI4R.OUT Output generated by the program DCMC37R using the sample input SMP371.INP SMP371R.OUT Output generated by the program DCMC37R using the sample input SMP372.INP SMP372R.OUT

MISCELLANEOUS MS-DOS batch file to merge the FORTRAN components together to create the complete program DCMCIR COPYIR.BAT MS-DOS batch file to merge the FORTRAN components together to create the subroutine package DCMCISPR COPYISR.BAT MS-DOS batch file to merge the FORTRAN components together to create the complete program DCMC37R COPY37R.BAT

dancoff mc

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