ML18130A261

Cobra Iiic/Mit Computer Code Manual,Vepco Version.

ML18130A261
Person / Time
Site:	Surry, North Anna
Issue date:	08/31/1979
From:	Bowring R, Moreno P MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE
To:
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ML18130A262	List: ML18130A261 ML18136A095
References
PROC-790831, NUDOCS 7910240550
Download: ML18130A261 (284)

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I COBRA lllC/MIT

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,, *COMPUTER CODE MANUAL I.

I I VEPCO VERSION 50r-~6f3\

.36e/36<1 I AUGUST, 1979 t.tr \o--1e-1-9 I ~ IOLL!()51tlt I

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I I COMPUT::'.R COD::: ~*!A.NUAL I

'., March 1975 I

I :1ASSACHUS:::TTS DTSTITUT:S O? TECHNOLOSY 77 Massachusetts Avenue Cambridge, ~*!assachusetts 02139 I

Principal !nvestigato:r's:

I Robert W. 3owring Pablo ~1oreno I

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?repared. f o::s I Electric Fower Research Ins~::~-~

3412 Hillview Avenue*

I Palo Alta, California

?raj ec-: )!anager:

J~3J4 I 3urt A. Zalotar I

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,, AUTHORS AND CONTRIBUTORS I The present code COBRA IIIC/MIT was developed in two phases, I the first phase being sponsored by the Electric Power Research Institute (EPRI) and the second by New England Electric System I and Northeast Utilities Service Co.

The first phase was carried out by Robert Bowring and in I* this period the bulk of the modifications introduced in COBRA IIIC I were executed. Research Assistants who made contributions to the project in this first phase include John Bartzis and Chong Chiu.

I Programming assistance was provided by Himagshu Bhattacharya in the Information Processing Center, M.I.T. Many useful suggestions I were also made by the staff of Battelle Pacific Northwest Labora-I tories (BNWL), in particular, by Donald Rowe.

are gratefully acknowledged.

Their contributions I In the second ohase, some new capabilities were introduced into the code and small oroblems with the code prepared in the I previous phase were re~edied. ~his phase Nas carried out by I Pablo Moreno under the direction of Professor Neil Todreas. Use-ful suggestions from John Valente, Chong Chiu and Ehsan Khan are I* acknowledged.

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TABLE OF CONTENTS Chapter 1 - Overall Comparison of COBRA IIIC/MIT and Page I COBRA IIIC ................................. . 10 Chapter 2 - Outline of Improvements Incorporated in I

COBRA IIIC/MIT .............................. . 12 2.1 Reduction.in Running Time ............... . 12 I

2. 2 2.3 Dynamic Storage ......................... .

Polynomial Expressions for Physical 12

• I Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 New Correlations ........................ . 12 I

2.5 Analysis of BWR's in an Assembly to Assembly Basis ........................ . 13 I 2.6 Metal and Coolant Modal Average Power 13 2.7 Various Errors and Anomalies in COBRA IIIC I

were Remedied . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.8 Input Data Presentations 13 I Chapter 3 - Modifications Incorporated in COBRA IIIC/MIT ...

3.1 Reduction in Running Time ............... .

14 14 I

3 .1. 0 Introduction ..................... , . 14 I 3.1.1 Description of the Problem ....... . 14 3.1.2 Channel Topography 16 I 3.1.2.1 Channel Boundary Inter-action ................ . 16 *I 3.1.2.2 Channel Boundaries Within the Stripe ............ . 17 I

3 .1. 3 Setting the Array LOCA ........... . 18 3.1.4 Reducing the Size of the Striped Matrix ......................... . 20 I

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I TABLE OF CONTENTS - Continued I 3.1.5 Setting the AAA Array in DIVERT ...... . 21 3.1.6 Processing the AAA Array in DECOMP I and SOLVE ......................... . 22 22 3.1.7 Summary and Modifications ........... .

I 3.1.8 Tests and Results to Check the Reduc-tion in Running Time .............. . 23 I 3 .1. 8 .1 Test Cases . .. . . . . . . .. . .. . . . .. 23 3.1.8.2 Timing Method .. . . . . .. . . . . ... . 24 I 3.1.8.3 Timing Runs ... . .. . . . . .. . . . . . 25 3.1.8.3.1 Original COBRA IIIC . . . . 25 I 3.1.8.3.2 New Cross-Flow Solution. 26 I 3 .1. 8. 3. 3 Faster "Rest of Calcu-lation ..... , .. , ... , . . . 27 I 3.1.8.4 Discussion . . . . . . . . . . . . . . . . . . .

3.1.8.4.1 Result of Modification..

28 28 I 3.1.8.4.2 Prediction for Reactor Case . . . . . . . . . . . . . . . . . . 28 I 3.1.8.4.3 Cross-Flow Solution Time.

3.1.8.4.4 Running Large Cases......

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'I 3.1.8.4.5 Scope for Further Improve-ment................... 30 3.1.8.5 Summary and Conclusions . . ... .. 30 3.2 Increase in Array Sizes.................. 31 I 3.2.0 Introduction .................... . 32 3.2.1 Method of Dynamic Storage ........ . 32 I 3.2.2 Modifications ............. , ..... . 33 I 3.2.3 Common Lists .................... .

3.2.3.1 Blank COMMON .. , ...... , .. .

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TABLE OF CONTENTS - Continued I 3.2.3.2 Named COMMON, COBRA 1 ........ 34 I 3.2.3.3 Named COMMON, COBRA 2 ........ 34 3.2.3.4 Named COMMON, COBRA 3 ........ 34 I

3.2.3.5 Named COMMONS, LINK 2' LINK 3 35 *1

3. 2. 4 Subroutine CORE ...................... 35 3.2.5 Input Data 36 I

3. 2. 6 Running Time ....................... . 37 3.3 Polynomial Expressions for Physical I

Properties .............................. . 37

3. 3. 0 Introduction ....................... . 37 I 38 3.4 3.3.1 Physical Properties ................. .

Extra Correlations ....................... . 40 I

3.4.1 Smith Slip Ratio ................... . 40 I

3.4.2 Baroczy Two-phase Friction Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.4.2.0 Introduction ................ . 40 3.4.2.1 Description of Correlation ... 42 3.4.2.2 Form of Correlation for Coding in COBRA IIIC ............. . 43 3.4.2.3 Construction of Multiplier Array ..................... . 43 3.4.2.3.1 Stage 1: Calculate Physical Property Index (PPI)... 43 3.4.2.3.2 Stage 2: Calculate Multinli-ers (M) at G=l.O Mlb/ft2hr 4li 3.4.2.3.3 Stage 3: Calculate Multipli- 46 er at all values of G...

3. 4. 2. 3. 4 Coding Sequence .......... . 47 3.4.2.3.5 Multiplier Values ........ . 48

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,, TABLE OF CONTENTS - Continued I 3.4.2.4 Interpolation for G and X.. .. . . . 48 I 3.4.2.5 Accuracy of Coding Baroczy Functions. . . . . . . . . . . . . . . . . . . . . 48 I 3.4.2.5.1 Physical Properties.......

3.4.2.5.2 Multiplier at a Mass Velo-49 city of 1.0 MLb/ft2hr... 50 I

,, j 3.4.2.5.3 Mass Velocity Correction Factors.................

3.4.2.5.4 Interpolation.............

51 51 I 3.4.2.5.5 Overall Errors............

3.4.3 Thom Two-Phase Heat Transfer 51 Coefficients . .. 52 I

o ...... o ***** o ** o * * * * * *

• 3.4.3.0 Introduction.................... 52 I 3.4.3.1 The Equations of Thom et al.....

3.4.3.2 Use of Heat Transfer Coefficient 52 53 I in Code . . . . . . . . . . . . . , ...

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• 3.4.3.2.1 Heat Flux................. 53 3 . 4. 3. 2 ~ 2 JBOIL. . . . . . . . . . . . . . . . . . . . . 54 3.4.3.3 Modifications................... 55 I 3.4.3.3.1 PROP...................... 55 3.4.3.3.2 HCOOL (N, I, JJ)... ..... .. 56 I 3.5 Analysis of BWRs in an Assembly to Assembly Basis" ... o ** v ** Cl * , *** o ****** e **** o c ll " o o o" o o .. 56 I

,, 3. 5. O Introduction............................

3.5.1 Iteration Theory........................

3.5.2 Iteration Strategy......................

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.1 TABLE OF CONTENTS - Continued I 3.5.3 Coding................................ 59 I

3 . 5 . 3 . 1 IND AT ........................ . 59 I 3.5.3.2 CARDS4 and CHAN .............. . 59 3 . 5 . 3 . 3 SC HEM:E . . . . . . . . . . . . . . . . . . . . . . . . 60 I

3. 5. 3. 4 SEPRAT ..................... ~ .. 60 3.6 Fuel and Coolant Modal Average Powers ...... . 61

3. 6. 0 Introduction ......................... . 61 3.6.1 Power Input in the Original COBRA IIIC 62

3. 6. 2 Modifications ........................ . 63 I 3.6.2.1 IQP3 Trigger ................. . 64 3 . 6 . 2 . 2 QPR 3 ......................... . 64 I

3 . 6 . 2 . 3 HEAT . . . . . . . . . . . . . . . . . . . . . . . . . .

3 . 6 . 2 . 4 DIFFER ....................... .

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65 3,7 Various Errors and Anomalies in COBRA IIIC .. 65 I 3.7.1 Negative to Heat Flux irt PROP ......... . 65 3.7.2 Array out of Range in DIFFER ......... . 66 I 3.7.3 Initialisation Quirk in COBRA IIIC ....

3,7,3.0 Introduction ................. .

67 67 I

3.7.3.1 Initialisation ............... . 67 I 3.7.3.2 Modification to COBRA IIIC ....

3.7.4 Anomalous Behavior of COBRA IIIC Using 69 . ..,

the Subcooled Void Option when Bulk Boiling at Channel Inlet .......... .

3.7.4.0 Introduction ................. .

69 69

• I 3.7.4.1 Explanation .................. . 70 I

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I I TABLE OF CONTENTS - Continued I

I 3.7.5 COBRA IIIC Modification to Prevent Occasional Overflow in Subroutine SCQUAL................................ 71 I 3.8 ._-Input Data--for COBRA I-IIC/MIT ........ -..... -.....

3. 8. o Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . .

71 71 3.8.1 Input Data Presentation Based on the I COBRA IIIC Presentation............... 73 3.8.l.l COBRA IIIC Input Data........... 73 I 3.8.1.2 Simplified COBRA IIIC Input Data to be Used for Assembly to I Assembly Analysis of LWR......

3.8.2 New Input Data Presentation.............

74 75 I Chapter 4 - Description of the Organization of COBRA IIIC/MIT

,, 4.1 Code and of its New Subroutines..................

4. O Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Organization of the COBRA IIIC/MIT Code.......

77 77 77 I 4.1.1 Read in the Input Data.................. 78 4.1.2 Print the Input Data.................... 80 1- 4.1.3 Thermal/Hydraulic Calculations.......... 80 I 4. 2 4.1.4 Print Out of the Results................

Description of Subroutines. . . . . . . . . . . . . . . . . . . .

81 81 I 4 . 2 . 1 MAIN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2.2 INDAT ................................... 82 I

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• 3 INPRIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 . 2 . 4 CALC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 . 2 . 5 EXPRIN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82 83 83 I 4 . 2 . 6 CARD 2 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4 . 2 . 7 ITHO ........................ : . . . . . . . . . . . 83 I 4

• 2 . 8 CHAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 I

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TABLE OF* CONTENTS - Continued

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4.2.9 MODEL .................................. . 84 I 4 . 2 . 10 0 PERA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.2.11 FIZPRP ................................. . 84 I 4.2.12 TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4. 2 .13 READIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85 85 I

4.2.14 TIDY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 I

4. 2 . 15 PRECAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.2.16 CARDSl ................................. . 85 I 4 . 2 . l 7 CARDS 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 402.18 CORE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. 86 I'

4.2.19 SEPRAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 . 2 . 2 0 QPR 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86 86

.I 4.2.21 ACOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 I 4.2.22 BAROC .................................. . 87

4. 2 . 2 3 SURTEN ......................... , ....... . 87 I

4. 2. 2 4 HAPROP ............................... , ..

4.2.25 Functions ROLIQ, ROVAP, HLIQ, HVAP and 87 I

SATTEM" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 5 - Presentation of Results ........................... .

87 88 t

5. 0 Introduction ................................. . 88 *1

5. l COBRA IIIC ................................... . 88 5.2 COBRA IIIC/MIT with the Old Input Data Presen-tation ....................................... 89 I

5.3 COBRA IIIC/MIT with the New Input Data Presen-tation ......... o ............................. . 89 I Chapter 6 - Listing of the COBRA IIIC/MIT Code ................ . 90 1.

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I ---**-*--*-- -.-***-------- *------- - -* **--- -SA-LIST OF FIGURES I

Figure 1. Channel and Boundary Numbering Scheme 93 I Figure Figure

2. Channel and Boundary Numbering Scheme 3 . Channel Layout for 10 to 128-channel cases 94 .

95 I Figure 4 . Baroczy Two-Phase Friction Multiplier at G = 1. 0 Mlb/ft2 hr. 96 Figure :J

• Baroczy Mass Velocity Correction to Two-r-

I Phase Friction ~ultiplier Figure 6. Physical Property Index (PPI) vs. Pressure 97 PPI = (µ 1 /µg)0.2/(p1/Pg) 98 I Figure 7. Baroczy Two-Phase Friction Multiplier at G = 1.0 Mlb/ft2hr. .99 I Figure 8 . Baroczy Mass Velocity Correction to Two-Phase Friction Multipliers 100 Figure 9. Organization of COBRA IIIC/MIT 101 Figure 10. Organization of the Reading of the Data When Card Group 20 is Selected 102 Figure 11. Organization of the Reading of the Data I When Card Group 20 is Not Selected Figure 12. Arrangement of Channels and Rods in the 103 I Example Problem 104 LIST OF TABLES I Table 1. Comparison of Storage Requirements and Costs With Problem Size Using COBRA IIIC/MIT on an I Table 2 .

IBM 370/168 LOCA Array for Case of Figure 1 105 106 I Table 3.

Table 4.

LOCA Array for Case of Figure 2 Timing for Original COBRA IIIC (10 Axial

• 107 Intervals) 108 I Table 5. Timing With New Cross-Flow and New nRest 11 Subroutines (10 Axial Intervals) 109 I Table SA.

Table 6.

Running Times per Iteration - in seconds Coordinates of Two-Phase Pressure Drop 110 Correlation 111 I Table 7. Coinparison of Actual and Calculated Values of PPI 112 I ~*-*-*_.- . ----~~ab le 8.

Table 9-. -*--

Value of n in M = 1-X + Xn/PPI 113

• -v:a:-1u~-s of *-*th~- **=*I~~~ Veloci_t_y c~-~rectio~ "::_~-=------~-~~:

Factor for Interpolation Between in ~ig. 9 114 I Table l:J.

Table 11.

Multiplier Arrays at Various Pressures Comparison Between Costs of COBRA IIIC and 115 COBRA IIIC/MIT for the Problem of Fig. 12 116 I

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APPENDICES I Page I

1. Subroutines ACOL, DIVERT, DECOMP and SOLVE 117 .

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Input Data for 32-Channel Case Timing Method 124 127 I

4. Faster "Rest of Hydraulic Calculations" 131 I

5. Subroutine CORE and BLOCK DATA 1341 6.

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Subroutine ZIGET Physical Properties Subroutines Coding of Subroutine BAROC 139 146 149 9.

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SEPRAT Coding Input Data Presentation based on that of COBRA IIIC 153 156 I

11. Simplified COBRA IIIC Input Data Presentation to be used for Assembly to Assembly Analysis of LWR 176 I

12. New Input Data Presentation 211 I

13. Results obtained with COBRA IIIC for the example problem 271

14. Results obtained with COBRA IIIC/MIT (Old Input Data Pres en-tat ion) for the example problem I

383

15. Results obtained with COBRA IIIC/MIT (New Input Data Pres en-tation) for the ex~mple problem 498 I

16. Coding of Timing Subroutine PRNTIM 619 I

17. Subroutine DIFFER 622 18.

Listing of the COBRA IIIC/MIT Code 626 I I

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I I I CHAPTER 1 I OVERALL COMPARISON OF COBRA IIIC/MIT AND COBRA IIIC COBRA IIIC/MIT was developed, primarily, to be the thermal-I hydraulic part of MEKIN(l), a neutronic-thermal/hydraulic code I

developed at M.I.T. by J. Stewart and R. Bowring. For this pur-pose, it was necessary to adapt a thermal-hydraulic code able to-analyze LWR.s using 200 channels to simulate the core.

COBRA IIIC was the code selected at the starting point. The I idea was to keep the same conservation equations (i.e. mass, I energy and momentum) and the same basic organization of the

., code but make modifications in COBRA IIIC as necessary to solve such big problems. Also chang~would be made to resolve some minor problems in COBRA IIIC and to introduce a streamlined method I of Data Input.

I It was planned then, that COBRA IIIC/MIT should yield identi-cal results to those of COBRA IIIC when applied to the same I problems, but the spectrum of problems tfiat could be economically analyzed with COBRA IIIC/MIT would be much larger, and even for I the same problems, some improvements would result.

I The two main characteristics of COBRA IIIC/MIT compared with COBRA IIIC, are its lower running time and the use of the Dynamic 1* Storage Data Management scheme developed at the Savannah River Laboratory. These two factors make possible the*simulation of I

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cases with a rather large number of channels at a reasonable cost. I As an example, in Table 1 the storage requirements and the cost of three cases analyzed using COBRA IIIC/MIT with an IBM 370/168 I

computer are presented. Comparative requirements for COBRA IIIC I are not included since the 30 and 101 channel cases cannot be run with this code. I Some other minor characteristics are also introduced, all of which will be described in full detail in Chapter 3. They I

are outlined in Chapter 2 to provide the reader with the necessary general picture of the improvements.

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I I 'I 2.1 CHAPTER 2 OUTLINE OF IMPROVEMENTS INCORPORATED IN COBRA IIIC/MIT Reduction in Running Time I The most important characteristic of the present code is I the reduction in running time.

reduction by taking adv~ntage It is possible to achieve this of the sparsity of the cross-flow I. matrix while keeping basically the same method of solution as in COBRA IIIC. This change makes it possible to analyze cases I with up to 200 channels at a reasonable cost.

'I 2.2 Dynamic Storage The dynamic storage data management scheme developed at the I Savannah River Laboratory is used in this version of the code.

I Utilizing this scheme the code itself sets the computer space required for each particular case.

I 2.3 Polynomial Exnressions for Physical Prooerties I While in COBRA III.C the physical properties of the wate:::' and

• steam need to be inpute~ in COBRA IIIC/MIT such properties are II calculated within the code from polynomials at pressures specified by the Input Data.

I 2.4 New Correlations I Three new correlations were introduced. These are the Smith Slip Ratio, ~he Baroczy Two-Phase F~iction Pressure Drop and the I Thom Two Phase Heat Transfer Coefficient.

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2.5 Analysis of BWRs. in an Assembly to Assembly Basis A different iteration strategy was programmed for BWRs since for them, there is no interconnection between fuel

'I assemblies. I 2.6 Metal and Coolant Modal Average Power COBRA IIIC does not allow different axial profile fluxes I

for different channels. This limitation was removed in COBRA IIIC/ t MIT where it is possible to Input different profiles for differ-ent channels by giving the heat generated in each node of the I core either for steady state or transient conditions.

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2.7 2.8 Various Errors and Anomalies in COBRA IIIC were Remedied Input Data Presentation In order to economically analyze cases with a large number of I channels, some modifications are needed in the original Input Data Presentation of COBRA IIIC since it requires too many cards I

to describe the problem.

were made available.

In COBRA IIIC/MIT, two general options One is actually that of COBRA IIIC but-with I

a new alternative available for assembly to assembly analysis of *I LWRs. The other is designed for problems where a rather large number of channels are used. It gives a. large reduction in l

Input cards.

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I I I CHAPTER 3 MODIFICATIONS INCORPORATED IN COBRA III-CC.MIT)

I* 3.1 Reduction in Running Time

1 3.1.0 Introduction I It had been suggested by BNWL personnel that the running

,, time of COBRA IIICC. 2 ) increased as the cube of the number of channels. This was due to the time spent in subroutines DIVERT, DECOMP and SOLVE in triple nested Do Loops to solve the set of I cross-flow simultaneous equations. Improvements had been made in COBRA IV by (a) modifying the method of constructing the coeffi-I

,, cient matrix and (b) using an iterative method of solving the equations instead of partial decomposition. This gave a running time increasing more nearly linearly with the number of channels.

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., As a result of this, it became clear that the original COBRA IIIC would have a prohibitive running time for reactor cases of (say) 200 channels and hence the code would need to be modified.

I .. The problem was examined at M.I.T. and the modifications are based on (~) a verbal description by BNWL of their more efficient I' way of constructing the matrix and (b) an M.I.T. technique of solving the equations using basically the same method as before I but taking advantage of the sparsity of the matrix. (3)

I 3.1.1 Descriotion of the Problem The hydraulic equations may be written down in such a way I that for an axial interval, 11 guessing 11 the lateral pressure I

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difference between channels, the cross-flows may be expressed as I

a set of N simultaneous equations, one for each boundary in turn, I b =

N=l

~

I k

l=l I

when W. = cross-flow across jth boundary J

bk~ akl = coefficients. I In the original COBRA IIIC, the coefficients akl and bk are calculated in DIVERT. The matrix akl is decomposed with partial pivoting in DECOMP to give all zeros below the diagonal. The

'I equations are solved in SOLVE to give the values of Wj.

The original method is wasteful in .running time because no I

account is taken of the sparsity of the matrix ak .

1 In a big .I problem, the vast majority of the values of akl would be zero because there is assumed to be no direct interaction between I channels sufficiently separated. However, these values of akl are calculated to be zero by the computer whereas it would be more I

economical to set them to zero. Furthermore in decomposing and I

- solving the matrix, every element has to be tested to see whether it is finite or zero.

It is this multiplicity of operations which I gives the excessive running time.

In the new method, firstly the boundaries influencing a parti-I cular boundary are identified and values of akl only calculated for these; the remainder are set to zero. Secondly, the boundary I

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'I* numbering scheme is organized so that finite coefficients of akl lie in a diagonal stripe, all *coefficients outside the stripe being zero. This striping" technique was suggested by I Kent Hansen. ( 3)

I 3.1.2 Channel Tocograohy 3.1.2.1 Channel Boundary Interaction. The cross-flow I equation for boundary i-j involves the conditions in the channels

• 1 i and j forming the boundary. The conditions in channel i are determined by the local effects and by interaction across the I four boundaries (square lattice assumed) i-j, i-i , i-i 2 , i-i 1 3

,I with the four adjacent channels, j,.i 1 -i . Similarly the conditions 3

in channel j are determined by the local effects and interactions I across the four boundaries j-i, j-j , j-j 2 , j-j . Thus the equation 1 3 for w j contains terms involving the other six boundaries i-j 1 ,

1 I i-j , i-j , j-i , j-i , j-i ; no other boundaries influence the 2 3 1 2 3 equation for wlj" I This is illustrated in Figure 1. Boundary 9 is between channels 6 and 7. Channel 6 is bordered by boundaries 5, 8 and I 12 and channel 7 by 6, 10, 13. Thus the equation for boundary 9

'I. contains terms from boundaries 5, 6, 8, 10, 12, and 13. For a square lattice geometry, the maximum number of "other boundaries" I is 6 and it may be smaller for edge channels (e.g. boundary 5 is influenced by only five others, namely, 1, 2, 8, 9, 12).

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When generating the matrix akl' only those values of l I

appropriate to k are used to calculate a; all other values of a I

are set to zero. The information relating k and l is stored in the array LOCA. I 3.1.2.2 Channel Boundaries Within the Strine. The I positions of the non-zero elements of the array akl depends upon the numbering system used for the boundaries and thus is under the I control of the User. It is then necessary to find a system which will minimize the width of the diagonal stripe in the matrix.

I It is considered that the best method is that illustrated in Figure 1, i.e. numbering left to right, top to bottom. Boundary 9 I

is influenced by boundaries between 5 and 13 (i.e. 5, 6, 8, 10, 12, I

13) so that the stripe width would be 8 (= 13-5). However, boun-dary 12 is influenced by boundaries between 5 and 19, i.e., a I

stripe width of 14, and this would be the maximum value.

if there are N channels arranged as a square, there would be In general, IN I

channels in a row and the stripe width would be 4/N - 2. I In decomposing the matrix and solving the equations, it is only necessary to operate within the stripe width. One would then I expect the number of operations to be proportional to the product of the number of boundaries and the stripe width, i.e. approximately I

to N3 12 instead of between N2 and N3 if the whole matrix must be searched. For up to 10 channels, one would not expect any gain as the stripe width is comparable to the number of boundaries, but

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,. there should be a considerable gain in large problems.

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The COBRA Input Data has been modified( 4 ) so that the I channel boundaries would be ordered as in Figure 1.

I 3.1.3 Setting the Array Loca I The array LOCA contains two sets of information. Firstly, it relates a particular boundary to the up-to 6 secondary boundaries I* which can influence it (as described in Section 3.1.2.1).

Secondly, it gives the sign of the cross-flow term. The I convention used in COBRA is that for two channels I and J, the I cross-flow direction I-J is taken to be positive when I < J and negative when I > J. Consider the coefficient akl where k is I the principal boundary I-J and 1 is the secondary boundary J-M.

After computing the value of akl it is multiplied by S where I S = 1.0 6~ ~1:~~~~c6~ding to th~ rulei:

I S = -1.0 when I > J > M

{ otherwise S = 1.0.

or I < J < M; I The secondary boundaries in the LOCA array are given the sign of S.

This is a quicker way of setting S in the construction of the akl I matrix than calculating it ab initio each time.

The LOCA array is set in the subroutine ACOL (coding in I Appendix 1) immediately after the channel boundary Input Data are I read in. It is called from INDAT, CARDS 4 or CHAN depending upon whether the original, simplified or new Input Data presentation I is being used.

LOCA (NK,8), where NK =number of channel boundaries is set I as follows:

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LOCA(K,l) = K (i.e. the principal boundary) I (LOCA (K,L), L = 2,7) = secondary boundaries; if none, I

set to zero.

above.

Sign as discussed LOCA(K,8) =Total number of boundaries.

The boundaries of LOCA are illustrated in Table 2 by consider-j' ing some of the boundaries in Figure l.

The method of setting LOCA is as follows:

I Do Loop K = 1, NK (number of boundaries)

I LOCA(K,l) = K (LOCA (K,L), L = 2,7) = 0 I Identify II and JJ, the channels defining boundary K. ,,,

Test all boundaries in inner DO Loop by identifying their channels III and JJJ. If either III or JJJ coincide I

with II, then a secondary boundary has been located and is stored in LOCA. It is given the sign of I (II - LL)/(II - JJ) where the three channels are LL, II, JJ.

I',

Repeat inner Do Loop, reversing II and JJ, testing against I'

old JJ.

Set LDCA(K,8) to number of boundaries. I End Do Loop.

The array name and size were chosen to make them the same as 1 used in COBRA IV. The size could have been (NK,6) since LOCA(K,l) = K I'

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.I I is superfluous and the information stored in LOCA(K,8) could be obtained by testing for the number of non-zero elements. However, I the COBRA IV size has been used to simplify any future incorpora-I tion of the code into MEKIN. The subroutine ACOL was programmed without reference to the COBRA IV coding. COBRA IV probably I

,, does not use the negative sign convention in LOCA but calls the function S(K,I) to find the sign of akl' Subroutine ACOL ends by (a) calculating MS, the stripe width

1. and (b) checking that enough storage has been allocated for the array AAA.

I In cases where IPILE = O, which imply that we may have more than four channels surrounding any single one, the LOCA array was I

,. changed to allow for the account of these channels.

array is now for these cases (LOCA (K,L), L = 1,14).

The new LOCA This change will permit the simulation of cases like the one described in I Figure 2 for which the LOCA array is that of Table 3. It is clear

-that with this array a wider number of cases is covered but that

• I number is limited and in some problems the split of channel 4 I (in several channels) may be needed in order to keep the array inside the 14 spaces.

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,. 3.1.4 Reducing the Size of the Strioed Matrix With the boundaries numbered as described in Section 3.1.2.2, the non-zero elements of the matrix of akl coefficients would be I within a diagonal stripe of width MS (calculated in ACOL). It is I

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only necessary to store the numbers within the stripe and these I

may be contained in an array of size (NK, MS); for most cases I this would be smaller than (NK, NK).

To use the smaller array, an element AAA (K,L) in the square I array is located at (K,MID-K+L) in the smaller array where MID is the mid point of the stripe, i.e., MID= (MS+l)/2.

I Without dynamic storage, the full benefit of the reduced size of the AAA array cannot be achieved. The array is set in MAIN as I

a single array and brought to DIVERT via SCHEME through argument I lists. In DIVERT, it is set as a double array of size (NK,MS) and carried through to DECOMP and SOLVE via argument lists. This gives I

some flexibility in that the amount of the array used (and thus running time) and its shape can be problem-dependent. Note that I

a check was made in ACOL that the product NK*MS did not exceed I the available storage.

I 3.1.5 Setting the AAA Array in DIVERT The coefficients akl in the AAA array are set in subroutine I DIVERT. It has been modified primarily by replacing the triple nested Do Loop (DO 80 K = 1, NKK) by a single Do Loop (DO 310 K=l, I

NK) - see Appendix 1. The procedure to calculate AAA and B is the same except (a) only the relevant boundaries, as stored in LOCA, I

are scanned, (b) for convenience the statement Function ABIT is 1 used .and (c) the diagonal stripe is set into a smaller array as described in Section 3.1.4. Other modifications to DIVERT are I I

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a relatively trivial.

I 3.1.6 Processing the AAA Array in DECOMP and SOLVE The AAA array is decomposed with partial pivoting in DECOMP.

I The subroutine has been modified by (a) removing the pivo~ing I because of the strong diagonal dominance, (b) only scanning within the diagonal stripe (this saves running time) and (c) the diagonal I stripe is set into the smaller array as described in Section 3.1.4.

In SOLVE, the modifications are similar; only the diagonal I stripe is scanned and the smaller array is used.

I 3.1.7 Summary of Modifications MAIN: Set AAA as a single dimension array of size I (NOW INDAT) MA (temporarily MGxMG)

Set MA Call ACOL from Card Group 4 coding I CARDS 4 OR Call SCHEME with AAA in argument list Order boundaries CHAN: Call ACOL I ACOL: Set LOCA from boundaries. Calculate MS I SCHEME: AAA in argument list Call DIVERT transferring AAA through argument I DIVERT: Rewritten. AAA transferred through argument, NK through COMMON and.MS through COMMON/

MEKIN.

1 Set AAA (NK,MS) using LOCA, thus avoiding unnecessary calculation of zero elements DECOMP: Rewritten. AAA transferred through argument I (thus eliminating COM..MON/BUL). Matrix de-composed, only scanning within diagonal stripe to save running time.

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SOLVE: Rewritten. AAA transferred through argument.~

Equation solved only scanning within diagonal shape to save running time.

I 3.1.8 Tests and Results to Check the Reduction in Running Time I

3.1.8.l Test Cases. Test cases with 10, 16, 32, 64 and 128 channels were constructed. The channels were typical of a I PWR assembly with a flow area of 37.43 in 2 and containing 264 rods.

They were identical in geometry but their radial power factors I

varied between 1.003 and 1.182 and were distributed about lines I

of symmetry (Figure 3). Thus all cases should give identical results for the 10 basic channels (lettered A-J in Figure 3) - this I was checked - and should follow the same calculation path; this gives a valid basis of comparison between the running times for I

various cases. For economy, only 10 axial intervals were used.*

I A steady state calculation, requiring one hydraulic iteration, was followed by a transient calculation requiring seven iterations. I The Input Data for the 32-channel case are reproduced in Appendix 2 ; note that the simplified presentation (Appendix 11) of I

the original COBRA IIIC input Data Presentation is used for Card Group 1 (fluid properties) and for Card Groups 4, 7, and 8 (channel I

parameters). The channel arrangement. is in a 4 x 8 rectangular I matrix with four symmetrical quadrants (Figure 3).

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I 3.1.8.2 Timing Method. The timing method is detailed in Appendix 3, Briefly, a new subroutine PRNTIM (I) was called I from strategic points in the program, the calling position being I identified by the value of I from 0 to 8. The subroutine called TIMING (ITIM) to obtain the CPU time in centiseconds.

I Using PRNTIM, the following were printed: (a) the time between entering and leaving SCHEME (i.e. the total time per hydraulic I

,. iteration) and (b) the sum of the times spent between entering and leaving DIVERT (i.e. the total time per iteration spent in solving the cross-flow equations). The times given in Tables 4 and 5 are I 11 Cross-flow" = (b) and "Rest"= (a) - (b).

The following precautions were taken to obtain representative I times.*

Printing Time: The times at successive calls to PRNTIM were I stored and processed within the subroutine but not printed I until after the conclusion of the hydraulic calculations.

This avoided confusing the lengthy printing time with the I time being measured.

Comoiler: The results given in Tables 4 and 5 are for subrou-I times compiled using the H Compiler. It was found that its I code optimisation capability reduced the running time of the cross-flow subroutines by nearly a factor of 2 (0.52 to 0.28 I sec. for the 32-channel case) compared to the cheaper G Compiler which was_ used during modification development.

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Variation Between Runs. Nominally identical runs gave slightly different times when repeated. The variation between individual sections of computation was random up to

.I 10%, but the variation of the average time per iteration was 'I smaller, up to (say) 5%; for example, the average times for the 32-channel case in successive runs were 0.275, 0.275, I 0.278, 0.285 and 0.289 seconds. When several results were available for the same case, those presented in Tables 4 and I

5 are for the median run of the set.

I Because of its importance in extrapolation to reactor conditions, the 128-channel case in Table 5 was repeated. I The two times agreed within 1%.

Load Module Size. For economy, a "small" load module was fI used for the 10-, 16- and 32- channel runs and a "large" module for the 64- and 128-channel runs. As a check, the 32-I channel case was also run with the large load module; the I times agreed within 2% of the values with the small module.

I 3.1.8.3 Timing Runs.

3.1.8,3.1 Original COBRA IIIC: Timing runs I

were made with the original COBRA IIIC for 10, 16 and 32 channels; I cases with more channels were prohibitively expensive.

The results are given in Table 4, which also (a) compares I the times with values calculated from the.expression below and I

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I (b) gives the estimated times for a PWR case with 193 channels and 10 axial intervals. The IBM 370/168(MIT) computer was used.

I The results were fitted by the expressions below. The times I (seconds) for 10 axial intervals and per hydraulic iteration are given for (a) the solution of the cross-flow equations (Subroutines I DIVERT, DECOMP and SOLVE) and (b) the remainder of the hydraulic calculation (i.e. the time spent in subroutine SCHEME minus the

1. cross-flow solution):

I NC =No. of channels:

Cross-Flow: t =

NK =No. of gap boundaries 0.08 + 0.000235(NK) 2

• 8 I "Rest": t = 0.0027(NC)l.75 I 3.1.8.3.2 New Cross-Flow Solution: As said before subroutines DIVERT, DECOMP and SOLVE were replaced by versions with I improved coding taking advantage of the sparsity of the matrix.

The modifications consisted of:

I (a) DIVERT: Constructing the coefficient matrix AAA using I only relevant gap boundaries, setting the remaining terms to zero; previously the zeros were calculated.

I (b) DECOMP: Operating w~thin a diagonal stripe of width MS in the matrix; outside the stripe, all elements are zeros hence I need not be accessed. Previously all zeros were operated upon.

(c) DIVERT, DECOMP and SOLVE: The diagonal stripe was con-I tained within an array NK

• MS. This does not reduce the I running time but saves storage.

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Table 5 gives the timing results obtained with the new cross-I flow solution subroutines. By considering the three stages in the I solution (see Section 3.1.8.4.3), one may obtain an expression for the time as follows: I New Cross-Flow: t = 0.00282NK + 0.00000837 NK

• MS 2 I

+ 0.0000127NK 2 3 .1. 8. 3. 3 Faster "Rest of Calculation": It was noted that the running time for the Rest" in the original COBRA 1

IIIC increased as (NC)

• 75 (see Section 3.1.8.3.i) and was not pro-I portional to NC as one might have expected. This suggested scope I for further improvement and subroutines DIFFER and HEAT seemed the most likely candidates. I The modifications are described in Appendix 4. Briefly, DIFFER was modified by changing the order of calculation of the I

summed contributions from neighboring channels in the mass balance, I

heat and pressure drop equations. HEAT was modified for PWR and BWR cases only (in which there is a one-to-one correspondence I between rods and channels) by avoiding the unnecessary examination of the effects of other channels on each rod heat flux and power.

I Table 5 gives the results of the timing runs. The times were closely proportional to the number of channels (the number of boun-I daries is roughly proportional to the number of channels) and were I fitted by the expression:

New 11 Rest": t = 0.01 NC I

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I 3.1.8.4 Discussion.

3.1.8.4.1 Result of Modification. In the I original COBRA IIIC, the running time increased nearly as NC3

=

I where NC number of channels - Table 4.

it increases between Nc 1

• 5 and NC 2 .

In the modified version, This represents a reduction I in running time by a factor 3 for NC = 10, 25 for NC = 32 and 220 for a reactor case of NC= 193 (Tables 4 and 5).

I 3.1.8.4.2 Prediction for Reactor Case. For I a typical PWR with 20 intervals, the results in Tables 4 and 5 for 10 intervals should be doubled. Hence for the original COBRA IIIC, I the estimated time per iteration would be about 1.8 hours9.259259e-5 days <br />0.00222 hours <br />1.322751e-5 weeks <br />3.044e-6 months <br /> whereas I with the new version, it is reduced to about 30 seconds.

(say) 6 iterations, the time might be about 3 minut~s, Assuming costing I ---$36.-- *-----

I 3.1.8.4.3 Cross-Flow Solution Time.

would expect the time to solve the cross-flow equation to be made One I up as follows:

(a) Constructing the matrix: t ~ NK. It is constructed by I operating on the elements of the array LOCA (NK,8).

t ~ NK*(MS) 2 .

I (b) within Decomposing the matrix:

a triple-nested It is decomposed Do Loop on NK, MS and MS, i.e. for each I row of the matrix, the elements are traversed across and down the stripe width. In the original version of COBRA the

• 1 Do Loop limits were NK, NK and NK giving a running time nearly

~ NK3.

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(c) Solving the equations. The number of operations is I

(n + 1) in solving for the (NK-n)th boundary, hence the I total number of operations is proportional to NK(NK + 1) i.e.

for NK large, approximately NK 2 . I Based on this notion, it was found that the running time could be expressed in the form a NK + b NK MS 2 + c NK 2 where a = 0.00282, I

b = 0.00000837, c = 0.0000127. For the reactor 193-channel case I

in Table 5, the magnitude of the three therms is 1.01, 10.37 and 1.6. seconds; total = 12.99 seconds. Thus the middle term, which I one may tentatively associate with the time required to decompose the matrix, predominates.

I k2 Since approximately MS x NC and MK x NC, the two dominant terms give the solution time as approximately~ NC 2 , as was found I

in practice (see Section 3.1.8.4.1). Earlier predictions that the I time should be proportional to Nc 1

• 5 were based upon the misconcep-tion that the diagonal stripe was only traversed across, and not I down, when decomposing the matrix.

I 3.1.8.4.4 Running Large Cases. It is possi-ble that the 128-channel case is the largest ever run with COBRA IIIC; I

the running time using an unmodified version of the code would be I

high, a~out 15 min. per iteration.

It augurs well for the use of COBRA in MEKIN that no stability I problems associated with size were encountered and the number of iterations and answers were the same as for the 1/16 symmetry, I

10-channel case.

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I 3.1.8.4.5 Scope for further imorovement. The majority of the running time in large problems is taken in the I cross-flow solution (see Table 5).

I In decomposing the matrix, operating only within the diagonal stripe reduced the number of operations but it is still relatively I inefficient. For example, in the reactor case there were 356 (i.e. NK) element.s per row in the original matrix of which up to I 7 were non-zero. Use of the striped matrix reduced the number of I elements scanned from 356 to 59 (i.e. MS), This is a big saving, but of these 59, there are still at least 52 zeros which are I scanned unnecessarily.

An iterative method, such as used in COBRA IV, which only I operated on the finite elements in the matrix might be considerably I faster even though several iterations would be required.

other hand, there might be problems of numerical stability.

On the Further I investigation would be required to resolve these points.

I 3.1.8.5 Summary and Conclusions.

(a) Timing runs have been made for the original and modified I versions of COBRA IIIC. The modifications reduced the running time by a factor of 25 for a 32-channel case and by an expected I factor of 220 for a PWR case of 193 channels. For a PWR case with I 20 axial intervals, the predicted running times are 1.8 hours9.259259e-5 days <br />0.00222 hours <br />1.322751e-5 weeks <br />3.044e-6 months <br /> per iteration with the original COBRA IIIC and 30 sec. per iteration I with the modified version.

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(b) The subroutines modified were: I Cross-Flow Solution: DIVERT, DECOMP and SOLVE Hydraulic Calculation: DIFFER, HEAT I

The modifications to the cross-flow solution comprised (a)

I economies in constructing the coefficient matrix (b) operating within a diagonal stripe when decomposing the matrix. I The modifications to the rest of the hydraulic calculation involved summing the interactions between channels using a Do Loop I over the number of boundaries instead of the number of channels; this avoided IF tests of whether boundaries were relevant. Also, I

for PWR and BWR cases, the zero contribution of a rod to non-rele- I vant channels was not calculated.

(c) It is predicted that for a PWR calculation with 20 axial I intervals using the modified version of COBRA IIIC, the running time per iteration would be 26 sec. to solve the cross-flow equation I

and 4 sec. for the rest of the calculation. There would be little I to gain by further improving the "rest" but substantial gains might be possible if the cross-flow solution could be improved. It is I probably that the majority of time is spent in decomposing the matrix, 20.7 seconds out of 26, and since the time for this opera-I tion increases as NC 2 this accounts for the overall running time I

dependence.

3.2 Increase in Array Sizes I

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I 3.2.0 Introduction COBRA IIIC /MIT was written -using the Dynamic ( 5) Storage I Data Management scheme developed at the Savannah River Laboratory; I the storage allocation for each of the problem-dependent arrays is set according to the space required for the particular run being I made. Then the same version of the code can be used for small and large problems.

I 3.2.1 Method of Dynamic Storage I The technique, as applied to COBRA IIIC( 2 ) is described briefly below.

I Problem dependent arrays had earlier been identified( 6 ). These I were then combined into a single array DATA( ), the position in the array corresponding to the variable considered. Thus the I channel areas, which in the original COBRA IIIC would be written as (A(I), I=l,MC), became (DATA($A+I),I=l,MC), where MC =number of I channels and ZA is an integer. Thus, if ZA were present for the I run to (say) 3412 and MC=30 then the channel areas would be stored in DATA(3413) to DATA(3442). Double arrays were stored in a similar I way, e.g., the channel flow rates ((F(I,J),J=l,MX),I=l,MC) would be stored as DATA(ZF+I+MC*(J-1)), etc.

• 1 The convention was adopted that all names beginning with the Z sign were integers. Also all problem-dependent variables in the I original COBRA were prefixed by the Z sign to identify their I position in the array DATA; for 6-character variables the last was dropped, e.g., HPERIM became ZHPERI.

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At the start of a run, the addresses in the DATA array were I set in subroutine CORE (called from INDAT-Ref. 7), the maximum number of channels (MC), gap connections (MG), etc., being given I

as Input Data.

I 3.2.2 Modifications Every statement in COBRA containing a problem dependent array I

was identified (the H-compiler list of arrays was a help in this I

chore) and rewritten in the new form. Non-integer quantities were contained in that array DATA, integers in IDAT and logical quanti- I ties in LDAT were DATA(l), IDAT(l), and LDAT(l) were equivalenced.

Examples of the modifications are given below.

I Old Array Size New I A(I)

NTYPE(I)

• FDIV(K)

(MC)

(MC)

(MG)

DATA($A+I)

IDAT(ZNTYPE+I)

LDAT(ZFDIV+K)

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• LENGTH(I) (MC) DATA($LENGT+I)

F(I,J) (MC, MX) DATA(ZF+I+MC*(J-1))

TROD(L,N.J) (MN, MR, MX) DATA($TROD+L+MN*(N~l+

MR*(J-1)))

• In COBRA IIIC, in the above examples, FDIV was declared Logical and LENGTH Real, hence the use of LDAT and DATA respectively. I The problem dependent variables are identified in the Named Common COBRA3, described below. An example of dynamic storage I programming is given in Appendix 17 for subroutine DIFFER.

3.2.3 Common Lists I

All COM..MON variables and Own Arrays in the original COBRA IIIC I I

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I were collected together into four main Co~Jnon areas (see Appendix 17) with two other smaller Commons LINK2 and LINK3.

I 3.2.3.1 Blank COMMON. This contains only the array I DATA, to which are equivalenced the* arrays LDAT (declared Logical)

I and IDAT (declared Integer).

3.2.3.2 Named COMMON, COBRAl. This contains all I Scalar quantities in the original COBRA IIIC Commons.

I 3.2.3.3 Named COMMON, COBRA2. This contains all fixed arrays in COBRA IIIC, e.g. PP(30) (the values of pressure at which I physical properties are tabulated).

I 3.2.3.4 Named COMMON, COBRA3. This contains the I problem-dependent information.

MN, MR, MS, MX are given.

Firstly the values of MA, MC, MG, MA has been previously set to NK*MS I where NK =actual number of gap connections (<MG); MC, MG, MN, MR, MX are the maximum values of the number of channels, gap connections, I fuel nodes, rods and axial intervals respectively; MS is the stripe width of the AAA array in DECOMP (Section 3.1.4).

I Next follows 333, an integer denoting the number of positions, I currently 96, in the DATA array. This is followed by the positions themselves, e.g., SA (which gives the start of the storage area for I the channel areas) etc.

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3.2.3.5 Named COMMONS LINK2, LINK3. These contain I

the variables which were required to link together subroutines I INDAT, INPRIN, CALC and EXPRIN when they were separated in rewriting MAIN(?). LINK2 contains fixed variables (of COBRA2) and LINK3 I scalar quantities (of COBRAl). The original LINKl which contained problem-dependent arrays is not required as its information is I

contained in COBRA3. I They have been kept separate from the other Commons as they are not required in the thermal-hydraulic calculations but only I in the Input Data setting. Their contents are given in Reference 7.

I 3.2.4 Subroutine CORE Subroutine CORE (Appendix 5) computes the origins within the I DATA array of the old, fixed-dimensioned arrays A, NTYPE, etc.

is first called at the beginning of INDAT, immediately after a state-CORE I

ment setting the problem size, i.e., READ MC,MG,MN,MR,MX. I In Subroutine CORE the integer array ZLX(I) is used as the length of the old arrays A,NTYPE, etc. Values of ZLX(I) are comouted I for I=l,2, ... zzz, e.g.

ZLX(l) = length of the A array = MC I

ZLX(8) - length of the CCHAN array = MR*MX I In CORE the elements of the array ZORG(I) are effectively equiva-lenced to the origins in the COBRA3 common list, i.e.

I Z0RG(l) = ZA = origin of the A array I

Z0RG ( 2) = ZC_CHAN = origin of the CCHAN array I

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I The elements of this array are initially computed as Z0RG(l) = 1 I Z0RG(I) = Z0RG(I-l)+SLX(I-l) ; I=2,ZZZ I ZIGET is a subroutine written in assembly language (Appendix 6).

It is called for dynamic allocation of core space for the DATA array I (see Reference 5). The previously computed origins are incremented by the integer displacement returned to CORE from ZIGET, i.e.

I Z0RG(I) = S0RG(I)+KS-l; I=l,ZZZ In the first entry to CORE the length of the old array AAA has not I been computed. A second entry to CORE is made from ACOL(S) to I establish the length and origin of the array AAA, i.e. ZLX(2)=MA and

$0RG(2) = ZAAA-$0RG(l)+MA.

I If at e_itper entry to CORE, sufficient storage is unavailable an error message is written to indicate how much addition storage I is required for the problem.

I 3.2.5 Input Data I When using the Dynamic Storage version of COBRA IIIC, an extra Input Data card must be given before the normal. Input Deck, namely I Read MC, MG, MN, MR, MX (515).

when MC > Number of channels in problem I MG -> Number of gap connections (for BWR cores give MG at least 3 for the s*pecial use of the array SP during iteration)

I MN > Number of fuel nodes in problem (at least 1)

I MR > Number of rods MX > Number of axial intervals.

I Then follow the Input Data.

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3.2.6 Running Time I

The Dynamic Storage version of COBRA IIIC was checked against I the earlier version for various cases. The agreement with the printed values of enthalpy and mass velocity was exact and the I values of cross-flow agreed to five significant figures, i.e. the last digit printed might be different.

I The effect in timing was then investigated. The running I times for 16-, 32-, 64- and 128- channel cases were compared with those previously obtained( 9 )(Section 3.1.8). The results are I given in Table 5A.

The dynamic storage appears to have increased the running I

time slightly, from 14% for the 16 channel case to 4% for the I 128 channel case. This increase is considered to be acceptable.

3.3 Polynomial Expressions for Physical Properties I

3.3.0 Introduction I

The physical -properties of water and steam are calculated in COBRA IIIC by interpolating between values read in as Input I

Data at a set of discrete values of pressure. In COBRA IIIC/MIT I the physical properties, at some fixed pressure, are calculated from the polynomial expressions used in the subchannel code HAMBO I

and that have been programmed now in CIERA IIIC/MIT. These expres-sions have been used simply to generate the physical properties I

at fixed pressures instead of giving the values on cards, thus I retaining the interpolation method within-the program.

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I 3.3.1 Physical Properties The properties are coded (see Appendix 7) in a number of I functions and subroutines as follows:

I Liquid Density (lb/ft3) Function ROLIQ (P)

Vapour Density (lb/ft3) " ROVAP (P)

I Liquid Enthalpy (Btu/lb) " HLIQ (P)

-I Vapour Enthalpy (Btu/lb) " HVAP (P)

SATTEM (P)

Saturation Temperature (°F) "

I Liquid Specific Heat (Btu/lb°F) )

) Subroutine HAPROP Liquid Viscosity (lb/ft hr) )

I Liquid Conductivity (Btu/ft 2hr°F)

) ( P , H , CP , XMU , XK )

)

I Surface Tension (lb/ft) Subroutine SURTEN(P,RL,RG,ST)

Where p = pressure (psia)

I H = enthalpy (Btu/lb) - from HLIQ(P)

I CP = specific heat (Btu/lb op)

XMU - viscosity (lb/ft.hr)

I XK = thermal conductivity (Btu/ft 2hr°F)

RL = liquid density (lb/ft3) from ROLIQ(P)

I RG = vapour density (lb/ft3) from ROVAP(P)

I ST = surface tension (lb/ft)

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For numerical checking, values computed from the polynomials I

are tabulated below I Pressure 15 200 1000 2000 2500 I Temp. 213.15 381.99 544.68 635.87 668.14 Liq. Dens. 59,7887 54.3483 46.2835 38.8453 34.7882 I

Vap. Dens. 0.03803 0.43726 2.24609 5,33925 7.66218 I Liq. Enth. 181. 207 355,705 542.631 672.346 730.884 Lat. Heat 969.594 842.484 648.896 461.815 359,708 I Vap. Enth. 1150.801 1198.189 1191.527 1134.161 1090.592 Sp. Heat 1.00962 1. 07091 1.26524 1.64743 2.08775 I

Vise.

Th. Cond.

0.65919 0.39028 0.33974 0.38524 0.22546 0.18350 0.16945 I

0.32675 0.27480 0.25004 Surf. Ten. 0.004024 0.002666 0.001222 0.000464 0.000218 I I

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I 3.4 Extra Correlations The extra correlations included are:

I 3.4.1 Smith Slip Ratio I The Smith (10) slip ratio correlation is written as 1/2 I S = 0.4 + 0.6 {o. 4 + X (pL/pg o.4 + o.6x

0. 4)

}

I where S =slip ratio; X =quality; p1 ,pg = liquid and vapor densities.

I It is called by setting J3=2 in the Input Data thus adding to the existing options of J3=0 for S=l, J3=1 for the Armand/Massena I slip ratio.

Subroutine BVOID was modified by calculating the void fraction I from *the quality and the Smith slip ratio when J3=2.

I 3.4.2 Baroczy Two-Phase Friction Pressure Droo I 3.4.2.0 Introduction. The Baroczy correlation (11) is complicated to program involving (a) a physical property index as I a function of pressure and (b) interpolation in two graphs for the I property index, quality and mass velocity.

In COBRA the system pressure remains constant during the hydrau-I* lie iterations but may change during a transient. To minimize running time, an array is set at the start of the calculations I representing the multiplier at a given pressure, for various values I

I I

I I

of quality and mass velocity. This array is recalculated at the I

start of each time step when the pressure changes. During the I hydraulic calculation, the multiplier is found by interpolation within the array. I The coding for the correlation is contained within a new sub-routin BAROC (IPART,P,Q,GWV,FMULT,PPI) where IPART=l or 2; P,Q, I

GWV =pressure (psia), quality (O<Q<l) and mass velocity (lb/ft 2hr);

FMULT = ~equired multiplier, and PPI = physical property index.

I The coding of the correlation and its development is described I below. It is written so that a call to BAROC with IPART=l and P = system pressure sets the array. In subsequent calls to BAROC I with IPART=2, the mult~plier, FMULT, is obtained for the given values of GWV and W. The Baroczy multiplier is called by setting I

J4=2 as Input Data, thus adding to the earlier options of J4=0 for I homogeneous theory, J4=1 for Armand,* etc.

CALC in COBRA IIIC was modified by a statement: IF(J4.EQ.2) CALL I BAROC(l,PREF,O.O,O.O,RUB,PPI) immediately before the start of the iteration loop I

DO 430 NN=l NTRIES I VOID in COBRA IIIC was modified by a call to BAROC if J4=2, calculating the mass velocity from the flow rate DATA(ZF), thus I GWV = 3600.0*DATA(ZF+I+MC*(J-l))/DATA(ZA+I)

IF(J4.EQ.2) CALL BAROC(2,PREF,XP,GWV,DATA($PHI+I),PPI)

I The call is made with the other J4 IF tests e.g. between VOID0520 ~

and VOID0530. It returns with the interpolated multiplier DATA(ZPHI+I).

1.

I

I I I 3.4.2.1 Description of Correlation. Baroczy developed his correlation from experimental data for a number of fluids, e.g.

I boiling water, air-water, mercury-nitrogen, diesel oil-air, etc.

I He correlated the various fluids in terms of a Physical Property 2

Index (PPI) defines as (µ /µg) 0 * ;(p /pg) where µ = viscotity, 1 1 I p = density and subscripts l,g = liquid and gas.

He constructed a family of curves (Figure 4) for a mass velo-I city of 1.0 Mlb/ft 2 hr giving the two phase friction multiplier (M)

I versus PPI for various constant qualitites.

values of M vs. PPI and quality (X) -- Table 6.

He also tabulated I A second group of curves (Figure 5) gave a correction factor for four mass velocities (G), namely G = 0.25, 0.5, 2.0, 3.0 Mlb/

I ft 2 hr, versus PPI for various constant qualities.

A two phase friction multiplier is calculated knowing the I fluid, pressure (P), quality (X) and mass velocity (G) as follows:

I (1) From the pressure and physical properties, calculate PPI = (µl/µg)0.2/(pl/pg).

I (2) From PPI and X interpolate in Figure 4 to find the multi-plier at G = 1.0 Mlb/ft 2 hr.

I (3) From PPI, X and G, interpolate in Figure 5 to find the I (4) multiplier correction factor.

The required multiplier is the product of the value at I G = 1.0 (stage 2) and the correction factor (stage 3).

I I

I

I I

3.4.2.2 Form of Correlation for Coding in COBRA IIIC.

I In COBRA, the two phase multiplier is calculated I for each channel at each axial interval and for each hydraulic iteration. It is therefore important to use an efficient coding I technique to minimize the computer running time.

In the COBRA application, only water need be considered and I

the pressure remains constant for each time step. With these simplifications, the calculation of the Baroczy multiplier may be I

made in two steps. I (a) Once only, at the beginning of each time step, construct an array giving the corrected two phase multiplier at I

discrete values of quality mass velocity.

aga~nst discrete values of The 14 values of quality are O, 0.1, 1.0, I

3.5, 5.0, 7.5, 10, 15, 20, 30, 40, 60, 80, and 100%. The I 7 values of mass velocity are O, 0.25, 0.5, 1.0, 2.0, 3.0, and 1000 Mlb/ft 2 hr. I (b) Each time the multiplier is required during the hydraulic iteration, interpolate for G and X within the already I

constructed array. I 3.4.2.3 Construction, of Multiolier Array.

in the calculation are as follows:

The stages I

3.4.2.3.1 Stage 1: Calculate Physical Property I

Index (PPI). PPI is defined as (µ 1 /µa) 0

• 2 ;(p /p ) which is a function

- 0 1 g I

of pressure alone. .Examination of experimental data (Table 7)

I I

I I

I showed that PPI could be expressed as a functi9n of pressure as below. These values of PPI are compared with the values calculated I from the physical properties in Section 3.4.2.5.1 and plotted irt I Figure 6.

(p in psia)

PR = p/3204 I p < 1429.5 osia a = 2.46896 x 10 -4 , b = 0.195508, c = -0.03141 63 I d = 0.264363 (Al)

I I p > 1429.5 osia a = 0.220112, b = -0.299745, c = o.440706 I d = -0.325823 I* A . 3

= pR(a+bpR+cpR 2 +dpR )

PPI = A/[ 1. 0-pR+A]

I 3.4.2.3.2 Stage 2: Calculate Multipliers (M)

I at G=l.O Mlb/ft 2hr. Baroczy gives values of the multiplier (M) for various qualities and PPI, i.e., (µ /µg) 0

• 2;(p /pg) as in Table 6.

I 1 1 Each point in the Table may be characterized by a value of the I index n in the expression M = 1 - X+X n /(PPI)

I This expression tends to the correct limits of M=l at a 1* quality X=O and M=l/PPI at x~1.

narrow limits as shown in Table 8.

The index varies between fairly I

I

I I

For a given value of PPI, i.e., pressure, the value of Mat I each quality is calculated from the expression above with n ob-tained from Table 8 by interpolating for ln n versus ln PPI (over I

most of the range of PPI) at each of the required qualities. I The detailed method of calculating the mulitplier aat a given value of PPI and at each value of Xis as follows: I (a) If X=O.O, set M=l.O and if X=l.O, set M=l/PPI.

terpolate in Table 6 for each value of X between O and In-I 1.0 by the following method. I (b) If PPI < 0.001, find M by log-log interpolation in Table 6 between~*PPI = 0.0001 and 0.001. I (c) If PPI 0.3, find M by log-log interpolation in Table 6 between PPI = 0.3 and 1.0 .

I (d) For 0.004 < PPI < 0.03 and X < 0.10; quadratic interpola- I tion for n in Table 8. At required X, calculate n at PPI = 0.004, 0.01, 0.03. Express n as a quadratic in I PPI, i.e., ln(ni)=a.+b.lnPPI+c(lnPPI) 2 where

l. l.

I xi a.l. bi Ci 0.001 1. 2621 0.6749 0.073 I

0.01 1.9551 1.0043 0.1097 I

0.035 1.4985 0.8408 0.0971 0.05 0.7965 0.5531 0.0673 I 0.075 0.771 0.5638 0.0713 0.1 0.4838 0.4793 0.0657 I

I.

I

---

~ ----------

I I

I (e) Calculate M at X from value of n.

(f) For all remaining points, calculate n at tabulated values I of PPI above and below required value as* in Table 8.

I Find value of n by log-log interpolation on PPI.

M at X from value of n.

Calculate I 3.4.2.3.3 Stage 3: Calculate Multiplier at I all value of G. The curves of Correction Factor (F) vs. ln PPI as shown in Figure 5 were approximated by four straight lines. The I intersection was rounded off as illustrated below.

I c I F.J.- 1 - - -:::-1' I ., ,. _., ,.

,.. .,,,. I '

c ....

F.].

I -- ,I I -

- - -- -L I I E

I P.J.- 1 P.]. ln PPI I The two lines AC' and C'E intersect at C' where PPI=P..

values of PPI (P.J.- 1 , P.+ ) are selected such that lnP.J.- = lnP.-0.15,

].

Two

]. 1 1 ].

I lnPi+l = lnPi+0.15 (i.e., points Band D) and the corresponding values of the correction Fi-l'Fi+l calculated. Between Pi-l and Pi+l' the I correction is taken as the mean of the values on the lines BC'D and BD. Thus the values of correction calculated follow the line I ABCDE.

I I

I I

The correction factor (Fe) is taken to be linear with PPI I

between points:

I F c = zl z2 at PPI = 0.00026 0.0038 I

Z3 0.057 I Z4 0.198 1.0 1.0 I I

where the values of z for each quality are given in Table 9.

1 I

3.4.2.3.4 Coding Sequence. The construction of the multiplier array CORAB is coded in subroutine BAROC I (Appendix 8). The subroutine is entered with IPART=l and the coding sequence is:

I (a) From the pressure (P), calculate PPI as in Section I

3.4.2.3.1.

(b) Calculate the multiplier at G=l.O Mlb/ft 2hr at qualities I o, 0.001, 0.01, 0.035, 0.05, 0.075, 0.1, 0.15, 0.2, 0.3, 0.4, 0.6, 0.8, 1.0, as described in Section 3.4.2.3.2.

I The values of multiplier are set in the array (CORAB (I,4),

I=l, 14).

I (c) The correction factors are calculated within an outer DO I Loop on quality and an inner DO Loop on mass velocity.

The correction factor is 1.0 at both X=O and X=l.O for I I.

I

I I I all mass velocities -- cf. Figure 5.

. 2 For G=lOOO Mlb/ft hr, the correction factor~ are all set to 1.0 as indicated by I the trend of Figure 5 i.e., (CORAB (I,7), I=l, 14) = 1.0.

I The correction factors for G=0.25, 0.5, 2.0, and 3.0 Mlb/ft 2 hr are calculated as in Section 3.4.2.3.3. The multipliers at these I mass velocities are found by multiplying the value at G=l.O by the appropriate correction factor. The multipliers are then set in I the array (CORAB (I,J), I=l,14) where J=2-6 for G=0.25, 0.5, 1.0, I 2.0, 3.0. Finally, the multipliers at zero mass velocity are taken to be the same as at G=0.25 and are set in (CORAB (I,l), I=l,14).

I 3.4.2.3.5 Multiolier Values. Calculated I Values of the Multipliers are given in Table 10 fo~ pressures of 500, 1000, and 2250 psia.

I 3.4.2.4 Interpolation for G and X. Cross-plots were I made of the multiplier versus quality at various constant G, p and of the multiplier versus mass velocity at various constant G,. p.

I These showed. that it was reasonable to interpolate in the multiplier array linearly with quality, linearly with mass velocity below I G = 1.0 Mlb/ft 2hr. and linearly with reciprocal mass velocity above I G = 1.0 Mlb/ft 2hr. This is accomplished in the second part of the coding of BAROC (Appendix 8) using the statement function ZRECT.

I 3.4.2.5 Accuracy of Coding Baroczy Functions.

I I

I

I I

3.4.2.5.1 Physical Prooerties. Values of I

PL' pg' u1 , ug were obtained from References 12 and 13 Table 7 I gives (a) the values taken for the physical properties, (b) the values of PPI calculated from theproperties and from the polynomial I in Section 3.4.2.3.1 and (c) the error in the polynomial expression.

Table 7 shows that the error in the calculated value of PPI I

is less than 1% except below 250 psia and above 2500 psia. This I

is adequate for the reactor range of interest.

The polynomial values may also be compared with those used by I Baroczy. In his Table 1 he quotes the values of PPI he used for steam-water data at various pressures. These are tabulated below I

and compared with the values calculated from physical properties.

I o psia PPI (Baroczy) 590 0.033 1000 0.057 1400 0.083 2000 0.148 I

PPI (properties) 0.037 0.066 0.102 0.173 I It appears that Baroczy used values some 10-20% lower than the I

values calculated from the physical properties. It is not clear why I this should be so; an error of 10% corresponds to a 10% error in the density ratio or 60% in the viscosity ratio. The discrepancy I seems too high to be explained in terms of the expected differences between experimental data. If the discrepancy is genuine, the I

values of multipliers obtained from the Baroczy correlation at a I given pressure would be somewhat lower than the values Baroczy himself used in developing the correlation (see Figure 4). I.

I

I I

I 2 3.4.2.5.2 Multiolier at a Mass Velocity of 1.0 Mlb/ft hr. The calculated multipliers for the conditions in I Table 6 (except X = 0.005, 0.02) are correct since they were coded I as the data to interpolate between. The qualities 0.005, 0.02 were not given as data and the values calculated are tabulated below.

I p PPI Multiplier at G = 2

1. 0 Mlb/ft hr.

I psi a From Table 6 Calculated x = 0.005 0.02 0.005 0.02 I -- 0.001 5.80 16.o 5.31 16.1 I 'Vll 0.001 5.60 16.8 5.11 14.4 60 0.004 4.90 11.9 4.62 11.2 I 160 0.01 3.30 7.00 3.02 6.72 500 0.03 1. 55 2.57 1. 43 2.47 I 1400 0.1 1.12 1. 48 1.12 1.44 I 2600 0.3 1. 02 1.13 1. 03 1.14 I

I X =

The interpolation method results in small discrepancies at 0.005 and 0.02 between Baroczy values (Table 6) and those I calculated. However, since the calculated values are correct at the neighboring values X = O, 0.1 and 0.035, the integrated pressure I drop over a range of qualities would be only marginally in error.

I The values of the multiplier at intermediate values of PPI were I

I

I I

checked by using the computer graph-plotter to reconstruct Figure 4 I

to the same scale using subroutine BAROC -- see Figure 7. Super- I imposing the two Figures and holding them to the light, the lines coincided exactly (i.e. within, say, 3%) exceot for the small kinks I

= 0.03 at PPI in Figure 7. This and calculated values, confirmed the programming of the multiplier at G = 1.0 Mlb/ft 2 hr.

I 3.4.2.5.3 Mass Velocity Correction Factors.

I The coding of the mass velocity correction factors was also checked using the computer graph-plotter. The Baroczy curves given as I

Figure 5 were obtained by photocopying and magnifying. The computer I was used to plot to the same scale and the two sets of errors super-imposed and held to the light. After some trial-and-error fitting, I the two sets of curves agreed except over some of the regions I where two lines are paired one into the other (e.g. G = 0.25 Mlb/ft 2 hr.,

X = 10% to 20%, PPI = 0.057 in Figures 5, 8). Over most of the I curves, the agreement was within about ~2%.

3.4.2.5.4 Interoolation. Comparing the I

values of the multipliers obtained using the interpolation scheme I and the values from a curve joining several points, the maximum difference was about 3%. I 3.4.2.5.5 Overall Errors. For each stage in I the calculation of the multipliers, the error in the computer value is comparable with that of reading from the published Baroczy curves.

I This is considered acceptable. I.

I

I I I 3.4.3 Thom Two Phase Heat Transfer Coefficients I 3.4.3.0 Introduction. The fuel surface temperature in COBRA IIIC/MIT is calculated from Thorn's(l 4 ) modification of the I Jens and Lottes(l 5 ) superheat equation. This correlation was preferred to the Chen(l 6 ) boiling heat transfer correlation.

I We describe here the modifications to subroutines PROP and I HCOOL in COBRA IIIC.

I 3.4.3.1 The Equations of Thom et al. Based on experi-mental data, Thorn et al correlated the heated surface temperature I (Tw) under single phase and subcooled boiling conditions as follows:

I Single Phase 0 0 4 hsp = o.134(K/D) Re

• 65 Pr

• I Tw = Tb + 0/hsp I Subcooled Boiling Tw = Tsat + 0.07200.5/ep/1260 I h tp = (T w - Tb)/0 where I D =equivalent diafueter~(tt)

I hsp' htp = single phase and two phase heat transfer coefficient (Btu/ft2hr°F)

I k p

= thermal conductivity (Btu/fthr°F)

= pressure (psia)

I Pr, Re = Prandtl and Reynolds Numbers I

I

I I

= Wall temperature (°F) I Tb, Tsat 0

= bulk

= heat liquid and saturation temperatures (°F) flux (Btu/ft 2hr)

I These expressions were modified versions of the eralier cor-I relations of:

I Dittus-Boelter(l 7 ): hsp = o.023(K/D) Re 0

• 8Pr 0

• 4

-Jens-Lottes(l 5 ): Tw = Tb + 1.900.25/ep/900 I 3.4.3.2 Use of Heat Transfer Coefficient in Code. The I heat transfer coefficient is used twice in the COBRA calculations, namely to: I (1)

(2) calculate the rod temperature and heat flux, set JBOIL, indicating hte onset of subcooled boiling.,

I 3.4.3.2.1 Heat Flux. In COBRA IIIC, a forward I differencing scheme is used to obtain some of the quantities required in the heat balance equation, i.e., they are based upon values I

obtained for the previous interval. One of these quantities is I the heat transfer coefficient which is used to calculate the new rod temperature profile and the new heat flux. I These calculations are made in subroutine HEAT called from SCHEME, before the heat balance equation is solved, HEAT calls I

HCOOL to calculate the heat transfer coefficient using values, e.g., I heat flux, flow rate, etc., for the previous interval.

I I.

I

I I I HEAT then calls TEMP to calculate the rod temperature profile I from the heat transfer coefficient and the new heat generation within the fuel. Next, the heat flux is calculated from the heat I transfer coefficient and the wall-fluid temperature difference; the flux is then used in the heat balance equation to find the I interval-exit enthalpy.

The COBRA ~cheme has been retained although there is an I inconsistency. The heat transfer coefficient is calculated from I the heat flux from the previous interval and is then used to find the heat flux for the current interval. Ideally, one should I iterate so that the heat fluxes become consistent. However, this would only be necessary during boiling (when the heat transfer I coefficient is a function of heat flux). Under those conditions, I the surface temperature is only slightly above the saturation value and the error would only marginally affect the calculated rod I temperature profile.

I 3.4.3.2.2 JBOIL. The indicator JBOIL is ini-tially set to zero and then reset in PROP to the number of the I axial position (i.e., J) at which subcooled boiling could start.

This is determined as the point at which the surface temperature I calculated for single phase conditions would exceed the surface I temperature if boiling were occurring Tb + 0/h sp Tsat + ~T I >

sup I

I

I I

In the original PROP, hsD is calculated using the Dittus- I Boelter(l7) equation and the ~all superheat (~T sup ) from the Jens-Lottes(l 5 ) correlation. These are programmed in PROP. However, I

it seemed inconsistent to use different equations to set JBOIL from those used to calculate the heat flux. PROP has therefore I

been modified so that it now calls HCOOL to obtain the same set I of equations.

PROP is entered after the heat balance equation, hence in I calculating JBOIL the updated values of flow rate, heat flux, etc.,

are used to calculate the wall temperatures.

I It should be noted that JBOIL merely indicates the position at I which subcooled boiling could start and does not appear to have any effect upon the hydraulic calculations (it is used in CHF2 to cal- I culate critical heat flux). Steam generation is calculated to start using a different criterion, namely the subcooled boiling I

correlation, and this is not necessarily consistent with JBOIL. I For this reason, positive quality, rather than JBOIL, is used as the trigger in HCOOL to determine whether the single or two-phase I heat transfer correlations should be used.

I 3.4.3.3 Modifications.

I 3.4.3.3.1 PROP. Two cards in PROP are changed, namely the calculation of DATA(ZHFILM+I) and TLBOIL. I Card PROP0900 becomes:.

DATA(ZHFILM+I) = HCOOL(-1,I,J) I I.

I

I I ,,

I Card PROP0940 becomes:

TLBOIL = TF - DTWALL + HCOOL(-2,I,J)

For the first, HCOOL is entered with the trigger N=-1 and I returns with HCOOL = single phase heat transfer coefficient.

For the second, HCOOL is entered with N=-2 and returns with I HCOOL =wall superheat.

I 3.4.3.3.2 HCOOL(N,I,JJ). The function HCOOL replaces the dummy HCOOL in the original COBRA IIIC which set the I heat transfer coefficient to 5000/3600. The index N refers to the I rod number when called from HEAT and is a trigger when called from PROP. The indices I and JJ are channel number and axial position, I respectively; JJ=J-1 from HEAT and J from PROP - see Section 3.4.3.2.

For N=-1 (i.e., called from PROP), HCOOL is set to the single I phase heat transfer coefficient (hsp).

I For N=-2 (i.e., called from PROP), the two-phase wall superheat (Tw-Tb) is returned.

I For N > 0 (i.e., called from HEAT), hsp is returned for zero quality and htp for positive. quality.

I 3,5 Analysis of BWRs in an Assembly to Assembly Basis I 3.5.0 Introduction I COBRA IIIC is properly used for interconnected channels e.g.

I subchannels in a ro~ cluster or fuel assemblies in a PWR. The inlet flow to each channel is specified and the equations solved II I

I I

to give a constant exit pressure for each channel. Because of I the constraint of fixed inlet flows, the inlet pressures to each channel are not necessarily the same. It is found that for PWR's I

the solution is not sensitive to the inlet flow distribution I assumed because the cross-flow largely obliterates its effect after a few calculation intervals. I However, for a BWR, there is no cross-flow or interaction between assemblies and therefore errors in the given inlet flow I

could cause large errors in the solution obtained. It is necessary I to change the calculation strategy so that the channel flow rates are iterated to give the same pressure drop across all channels. I This note describes the modifications made to COBRA IIIC for BWR calculations.

I 3.5.1 Iteration Theory I For channel i, a flow rate of m.l lb/hr gives a pressure drop of pi psi. It is required to find a new flow rate Cm1 + om1 ) such I

that the pressure drop shall be p , where p 0 0 is the same for all I channels. This implies p 0 = pi. + (op.lorn. )om.].

I l ].

I

( 1) I I

I I

I I I From the mass conservation equation, Eomi = O, whence by I summing the set of equations for all channels:

= E(v.p.) ( 2)

I ]. ].

Substituting p form (2) into (1) for each channel I 0 (3)

I I 3,5.2 Iteration Strategy Equation (3) shows that if (op/om) is known for every channel, I the correction to the flow in each channel can be calculated direct-1 ly. Since there is a non-linear relationship between p and m, a number of iterations would be required.

I The value of v.]. for each channel is set to 6m./6P.

]. . ]. where 6p.,

].

6mi are the changes in pi and mi for each channel between successive I iterations.

I For the first iteration, an approximate value of vi is obtained from the following argument. The pressure drop across a channel is I made up of friction, acceleration, elevation and grid components.

Of these, all but the elevation component (6p ) can be written as I a power function of m:

e I

I whence

= (l/n)m I Vi D

. - 6p e I

I I

The value of n is approximately 1.8 in single phase, decreasing I

considerably in the two phase region. A compromise value of n is I 1.4 whence l/n = 0.7. The expression for v does not have to be accurate; it only has to start the iteration off in the right I direction. Thus we have:

I

( 4)

I Iteration 2 et seq.: vi= ~mi/~pi (5) where ~Pe = elevation pressure drop component I

~p, ~m = changes in p and m between iterations.

I 3.5.3 Coding I

3.5.3.1 In INDAT (nart of the old MAIN). BWR calcula-tions are called by setting IPILE=2 as Input Data. IPILE is a new I parameter and is given on the Control Card (see Appendix 11). The variable J7 is set equal to IPILE for transfer between subroutines I

via the Common List; any other purpose.

J7 was already in Common and was not used for I

The variable (WP(K),K=l,MG) is initialized to zero before I reading in the Input Data. This is w', the turbulent (fluctuating) cross flow, which is zero for separated channels. It would be I reset subsequently in PWR cases.

I 3.5.3.2 In CARDS 4 and CHAN. The channe~ Input Data are organized in this subroutine. For BWR's (IPILE=2), the interaction I

between channels must be suppressed. Firstly, each channel has no I

adjacent channels, i.e. ((LC(I,L),I=l,NCHANL),L=l,4)=0. Secondly I

I I

I NSCBC, NBBC, J5, ABETA, BBETA, GK are all set to zero; these are I respectively subcooled mixing option, two phase mixing option, thermal conduction option, two coefficients in the mixing expression I and the geometry factor for conduction.

I 3.5.3.3 In SCHEME. This subroutine contains the Do Loop over the channel intervals and organizes the hydraulic calcula-I tion. The modifications are:

(a) Set IPILE = J7 I If IPILE = 2 I (b)

(c) skip the call to MIX at card SCHM0820 Call SEPRAT (l,J,JUMP) after the heat balance equation; I thence skip the calculation of cross flow by jumping to the pressure drop calculation at card SCHM1300.

I (d) call SEPRAT (2,J,JUMP) immediately before RETURN.

I 3. 5. 3. 4 In SEPRAT. This subroutine .(see Appendix 9) is new and contains the bulk of the modifications required for BWR I calculations.

I In the first call to SEPRAT after the heat balance equation, the flow rate P(I,J) is set taking transient effects into account; I this is equivalent to card SCHM1190 but with DFDX=O. Then follows a call to DIFFER (3,J) to calculate the pressure gradient dp/dx I with zero cross-flow.

I The second call to SEPRAT comes after the channel exit pressure has been calculated. The calculation has converged if the fractional I difference between the minimum and maximum values of pressure drop I

I I

is less than the criterion FERROR set as Input Data (nominal value =

I 0.001). If the criterion is satisfied, the calculation returns to I SCHEME and thence to MAIN with JUMP=2 indicating convergence. If not, JUMP is set to 1 and new inlet flows calculated before I Returning.

The new inlet flows are calculated as follows. For the first I

iteration (a) the individual flow rates are summed to give FTOT, I

(b) v.]. for each channel is calculated from equation 4. In subsequent iterations, v.]. is calculated from equation 5. Next, rv.p.

]. ].

and rv.]. I are summed to give omi from equation 3 and thus the new mi. Finally, the values of F(I,l) i.e., m., ].

are corrected for accumulated I

rounding *off errors by summing and comparing with the original value FTOT.

I The array SP(MG,MX) is used for storing values between inter- I vals; its PWR use is to store pressure differentials between channels to calculate the cross flow but for BWR's, this use of I the array is not required. SP(I,l) is used for vi and SP(I,2),

SP(I,3) for storing the values of mi and pi from the previous I

iteration. I 3.6 Fuel and Coolant Modal Average Powers I

3.6.0 Introduction In the original COBRA IIIC, the total power is given via the I

Input Data as a function of time; the axial power profile is the -1 same for each rod. A second option has now been added to give the 1.

I

I I

I fuel and/or coolant heat generation rates as a function of time I for each nodal volume in the reactor; this implies that the axial power profile may be different for each rod.

I The following sections describes the modifications to COBRA IIIC and their testing .

.I 3.6.1 Power Innut in the Original COBRA III I In COBRA IIIC, the sequence of the thermal calculation is (a) Give power parameters via Input Data.

I (b) From SCHEME first call HEAT to calculate the heat flux I (FLUX (N,J)), fuel temperature and heat addition per unit length (QPRIM(I)) where I - Channel, N =rod and I J = axial station.

(c) From SCHEME, next call DIFFER to calculate the enthalpy I gradient DHDX (I) using QPRIM(I).

(d) In SCHEME, calculate the enthalpy at J from the heat I balance equation (card SCHM0900) giving void fraction, I mean fluid density, etc.

FLUX(N,J) is the important parameter that has to be calculated.

I It is used to calculate QPRIM(I), (for DHDX(I) calculation), sub-cooled boiling, CHF etc. In the original version of COBRA IIIC it is I calculated by another route but thereafter the calculations I follow the same course (except DHDX(I) includes the coolant heat generation where required).

I In the old method FLUX(N,J) is calculated in subroutine HEA~

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. I as a function of the Input Data parameter average heat flux (AFLUX),

I rod power factor (RADIAL) axial orofile (AXIAL) and the time factor I (POWER) (see HEAT 0520). If fuel temperatures are not required, FLUX(N,J) is used to calculate QPRIM(I) etc. However, if fuel I temperatures are required, then FLUX(N,J) is first calculated as above, i.e. from the input data, then it is used to calculate heat I

generation rate in subroutine TEMP (TEMP 0370), in which fuel I

temperatures are calculated. FLUX(N,J) is then overwritten and recalculated as a function of the temperature difference between I wall tempearture and fluid temoerature (HEAT 0790).

It is worth pointing out that in the input data the total I

power is given in the units of heat flux, but this is equivalent I

to either (a) Power generation rate within the fuel if temperature I calculations are to be performed.

(b) Average heat flux when temperature calculations are not I

to be performed.

• 1 3.6.2 Modifications The modifications to COBRA IIIC involve:

I (a) Set a trigger (IQP3) to indicate the calculation route I

and initialize QF and QC to zero.

(b) Preparation of a new subroutine (QPR3) to read in the I fuel (QF) and coolant (QC) heat generative rates.

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I (c) Modify HEAT to set FLUX and QPRIM.

(d) Modify DIFFER to include QC in the coolant heat balance I equation.

I 3.6.2.1 IQP3 Trigger. The trigger IQP3 is initialized I to 2 and the arrays of QF,QC to zero before reading in any Input Data. IQP3 may be reset in Card C8 through the value of Nl, i.e.

I the number of points along the channel at which the axial heat flux profile is specified.

I If Nl > 1: IQP3 remains equal to 2.

If Nl < 1: IQP3 is reset equal to Nl.

I The meaning of IQP3 in subsequent calculations is:

I IQP3 = O. Fuel heat generation (QF) given. Coolant deposition not given and remains set to zero.

I IQP3 = 1. Both fuel (QF) and coolant (QC) heat genera-tion given.

I IQP3 = 2. Normal Input Data and calculations.

I 3.6.2.2 QPR3. This new subroutine (QPR3) is called if IQP3 =0 or 1. This subroutine will read first ZM. If ZM is posi-I tive, the values of QF and QC (which will be given after ZM) are I all multiplied by ZM to convert to Btu/sec. If ZM = -1.0, the multiplier ZM is reset to 3413.0/3.6 so that QF and QC may be read I in MW and automatically converted to Btu/sec. If ZM = -2.0, it is rest to 1000.0/3.6, i.e., the conversion factor for MBtu/hr to I MBtu/sec. after ZM, the values of QF are read in and if IQP3 = 1, I

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the corresponding values of QC are also read.in. The values are I

then printed. I (1)

3. 6. 2*. 3 HEAT. The modifications to HEAT are:

Skip the calculation of QAX from CURVE (HEAT 0480)

I if IQP3 = 0,1; QAX is used to calculate fLUX and I this route is not requ~red.

(2) Skip the calculation of FLUX(N,J) from QAX (HEAT 0520) I

= 0,1; if IQP3 (N,J).

instead calculate FLUX (N,J) from QF I

3.6.2.4 DIFFER. Modify the calculation of DHDX (DIFF I

0500) to include QC in the enthalpy rise equation.

It should be noted that DIFFER (l,JJ) is called from SCHEME

'I to calculate the enthalpy rise with JJ = J-1, i.e. for th~ values I of the paz:ameters appropriate to the beginning of the axial interval being considered. The values of QC (I,J) read in corres- I pond to the interval J-1 to J, hence in DIFFER it* is nece~sary use QC (I,JJ+l) in order to obtain the correct values since JJ+l to

= J.

I 3.7 Various Errors and Anomalies in COBRA IIIC I

3.7.1 Negative Heat Flux in PROP I In a particular run, a failure occurred in which a negative number was raised to a non-integer power. Thi.s was traced to I

subroutine PROP, card PROP0940, in which QPRIM(I) was found to be I negative; QPRIM is the heat addition per unit length.

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I I I The physical picture was that in a transient, the fluid I temperature was specified, via the Input Data, to increase fairly rapidly. The fluid surface temperature increased with the heat I addition but less rapidly than the fluid temperature. The net effect was a negative heat flux, i.e. from the fluid to the fuel.

I The failure occurred in PROP when using the Jens and Lottes equation to determine whether subcooled boiling had started (this I contains q"**0.25, where qn =heat flux). For negative heat flux, I this test is clearly superfluous since subcooled boiling cannot

" occur if the surface is colder than the fluid. The cure was to I bypass the statement when the heat flux is negative:

Between Cards 2ROP0930 and PROP09&0, insert I IF (QPRIM(I).LT.0.0) GO TO 110.

I This modification leaves the physical model intact.

negative heat flux to occur (which it could in reality) but when It allows I it does, suppresses the test to see if subcooled boiling has started.

I 3.7.2 Array Out of Range in DIFFER I At the start of the calculation, when finding the inlet flow split between channels, subroutine SPLIT calls DIFFER (3,J) with I J = 1 (i.e. at inlet). In card DIFF0860, FLOWSQ is calculated I from F(I,JMl) where JMl = J-1, i.e. zero. Normally it does not matter what rubbish is calculated for FLOWSQ at inlet by this card I because by the next statement, if J = 1, it is recalculated.

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However, on rare occasions trying to fetch F(I,O) causes run I

failure. I The cure is to complete what the original programmer probably intended, namely to bypass the normal statement when J = 1. I Card DIFF0860 should be replaced by:

380 IF (JMl.GT.O) FLOWSQ = ABS(F(I,JMl)*F(I,JMl))

I 3,7,3 Initialisation Quirk in COBRA IIIC I 3,7,3.0 Introduction. Two identical cases run con- I secutively (in the same Run) using COBRA IIIC may give somewhat different answers. This is clearly undesirable and was found to I be due to incomplete reinitialisation between cases.

This quirk was discovered when checking that the ordering of I

the channel connections in the cr9ss-flow matrix had no effect I

upon the solution of the set of simultaneous equations. The order was not significant, but, in demonstrating it, the quirk I in COBRA IIIC at fi~st confused the issue.

The effect of the lack of initialisation in COBRA IIIC is I

fairly trivial and simple to put right.

the interests of complete documentation.

It is reported here in I

3.7.3.1 Initialisation. Quantities are initialised I

in COBRA IIIC before reading in the Input Data for the first case.

I For subsequent cases, the Data are taken to be the same unless changed, hence a complete reinitialisation before each case. would I I.

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I I I be undesirable. Since most non-Input parameters are recalculated, I the original COBRA IIIC contains no reinitialisation between cases.

Two identical consecutive cases gave marginally different I answers and this was traced to the lack of reinitialisation of the two arrays ((SP(K,J), W(K,J), J = 1, MX), K = 1, MG) = 0.0. Tests I showed that if both arrays were reinitialised, the answers were I identical but if either were not, the answers were different.

The array SP is the "guessed" differential pressure between I channels *and is updated between successive hydraulic iterations.

The initialised values of zero represent the first guess hence if I not initialised this represents an alternative first guess and is 11 not necessarily wrong 11 It is even arguable that if the second I

case is similar to the first, it might be better to use the results I of the first as the initial guess for the second. The differences in answers for the two first-guesses were found to be within the I convergence tolerance. Thus it would probably not be worthwhile since W must be reinitialised, it is considered better to reiniti-I alise SP too in the interests of consistency.

I The array Wis the cross-flow between channels. This is a calculated quantity and it is not obvious why its initialisation I should affect the answer. The only preset value is zero at inlet and this would not change during calculation.

I Time did not allow a detailed follow-up of why W required I

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reinitialisation. The results were consistent when SP and W were I

initialised to zero between cases and this allowed the more I important work to continue.

3.7.3.2 Modification to COBRA IIIC.

I (a) Remove the following cards from their original position I DO 915 K = 1, MG

• MAIN 5860 W(K,J) = 0.

WOLD (K,J) = O.

MAIN MAIN 5870 5880 I 915 SP(K,J) = 0. MAIN 5890 (b) Replace these cards, preceded by I DO 915 J = 1, MX between cards MAIN 6070 and MAIN 6080 (now in INDAT)

I' i.e. immediately before CALL DOY(DATE).

It may be noted that in the interests of coding simplicity, I

WOLD is unnecessarily reinitialised. I 3.7.4 Anomalous Behavoir of COBRA IIIC Using the Subcooled Void I Option when Bulk Boiling at Channel Inlet 3.7.4.0 Introduction. A COBRA IIIC case with bulk boiling at inlet was run using a deck of cards from a previous case which called for the Levy subcooled void option. This option i

should clearly have no effect for bulk boiling at inlet. In fact, I I

the void fraction calculation was anomalous. At low qualities, the calculated values were correct, then they decreased with increasing I

quality, reached a minimum and then rose again. Correct values were I obtained by not invoking the subcooled void option.

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I I I The reason for this behavior is given below. No modifications I were considered necessary to COBRA IIIC since it is only necessary to omit the subcooled void option when a case with bulk boiling I at inlet is run.

I 3.7.4.1 Explanation. In subroutine PROP, the single phase heat transfer coefficient HFILM is calculated by card I\ PROP0900_ only when the liquid enthalpy is below the saturation value. At the onset of bulk boiling, it is not recalculated but I* remains at the last single phase value. However, for bulk boiling I at inlet, it is never calculated hence takes the default value of 1.0E78.

I The heat transfer coefficient is used in subroutine SCQUAL to calculate DELTAT (Card SCQ0370) and thence the "quality" XD I at which subcooled void starts. Because HFILM is taken to be I large, XD becomes positive.

When the equilibrium quality Xe is less than XD, the void

• 1 fraction is calculated from Xe. When it is larger than Xd, the void fraction is calculated from (Xe-Xd). This gives a drop in I void fraction which then increases again with increasing Xe.

I Thus with bulk boiling at inlet and HFILM not set, the void fraction is calculated correctly up to some quality XD and then I drops to a lower value. If HFILM had been set to some nominal value, XD would have been negative and the effect of subcooled I void small but finite. Because the effect should be zero, it is better not to use the subcooled void option.

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3.7.5 COBRA IIIC Modification to Prevent Occasional Underflow I

In Subroutine SCQUAL I The Levy subcooled void correlation is programmed in COBRA IIIC in subroutine SCQUAL. Subcooled void starts when the equilibrium I quality (Xe) reaches a calculated negative value Xd. As Xe increases further, the subcooled non-equilibrium quality (X) in9reases 1*

from zero at Xd and tends exponentially to Xe according to the I equation

• I For Xd negative but close to zero and Xe large, the argument of I

the exponential can become large and negative when the computer will give an "Underflow" error signal.

I Under these conditions, the value of the exponential is, for I practical purposes, zero. Hence the cure is to set it to zero when the argument of the exponential function is less than some I

number (say) -15.0. This makes x The modification to SCQUAL is

= Xe.

I After the calculation of ARG and between Cards SCQL0450 I and SCQL0460, insert IF (ARG.LT.-15.0) GO TO 140. I 3.8 Input Data for COB~A IIIC/MIT I 3.8.0 Introduction I In the present version of the code two general options are 1.

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I I I available to input the data. The first option is based on the I original version of COBRA IIIC, and has two different possibi-lities, one for the analysis of a small number of subchannels I and the other for the analysis of the whole core of PWR's and BWR 1 s, each radial node being an assembly. The first possibility uses I exactly the same Input Data Presentation as COBRA IIIC, but for the second, card groups 4, 7 and 8 were lumped together to generate I a new card group 4. This modification is possible because in I such analysis many channels have identical characteristics and only the description of one channel is needed in order to describe I all the channels identical to this one. Also in this analysis, every channel is assumed to have a l~~ped rod that generates the I power introduced by the fission reaction in the channel. This I implies that the description of the rods and its power may be given in a more simplified way.

I Other improvements are made here which consist of the elimina-tion of the cards describing the physical properties of the coolant I that are calculated in COBRA IIIC/MIT by the code and then are I not required to be inputed.

The second option of given the Input Data is very useful in I the study of PWR's and BWR's, either in an assembly to assembly basis or a more detailed description of the core that allows for I the representation of subchannels together with lumped regions I and will make possible the study of the whole core in only one run.

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The arrangement of the Input Data is totally different in this I option which also has some other capabilities that the previous option does not. They are, for instance, the printing of the image I

of each card immediately after it is read, the use of the Baroczy I theory as a new option for the new-phase friction model, the possibility of introducing coupling parameter in the mixing term I of the energy equation and some other characteristics that provide a large range of flexibility in the division in channels of the I

whole core. With respect to the reduction in the number of cards required to describe the Input Data, this second option is even I

better than the second possibility of the first option. I The conclusion is then that the Input Data selected will depend on the case that is being analyzed. If this is a case with I

a small number of subchannels the original version of COBRA IIIC may be selected. If the case is the analysis of the core in an I

assembly to assembly basis either the second possibility of the II first option or the second option can be chosen but we recommend the second option because of its wider range of alternatives. I And finally for a more detailed analysis of the core, the second option should be selected.

I 3.8.l Input Data Presentation Based on the COBRA IIIC I

Presentation

• I*

3.8.l.l COBRA IIIC Inout Data. The code keeps the option of inputing the data as in COBRA IIIC. This option will -1 1.

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I I I be helpful in analysis of a few subchannels where the fluid is I not water or where some special characteristic, which in the other options were deleted, are needed.* The cards required I are described in Appendix 10.

I 3.8.1.2 Simplified COBRA IIIC Input Data to be Used for Assembly to Assembly Analysis of LWR. As the title suggests, I this option is based on COBRA IIIC but has some simplifications I when analyzing that PWR and BWR in an assembly basis are possible and very convenient because of the huge reduction in cards required I to describe the problem.

It is known that reactor channels (assemblies) tend to have I similar geometries and differ only in their powers and heat flux I profiles. Each rod is associated with one channel only (in a non assembly to assembly case, a rod may be bordered by several I subchannels); thus rod data may be given as part of the channel data. Also, one may remove the option for reading in wire-wrap I spacer data.

The Input Data presentation may be simplified by combining I the data given in Card Groups 4, 7 and 8 of the COBRA IIIC Input I Data presentation as follows:

(a) define several (up to 15) channel types in terms of their I geometry, rod dimensions and grids, (b) specify which channels are of which types, I (c) list the radial power factors of each channel, I (d) specify the interconnections between channels.

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The physical property data presentation may also be simplified.

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In the original COBRA IIIC, the properties at various pressures are I

read from cards. In the. new version, polynomial expressions are used to generate, within the program, the data which were originally l-read from cards.

The Input Data changes then with respect to the original 1*

version of COBRA IIIC and can be found in Appendix 11.

I 3.8.2 New Input Data Presentation This last option of giving the Input Data was developed for I

MEKIN, and then was further extended, because.of its simplicity, I

to be used in COBRA IIIC/MIT. It allows the description of problems such as analysis of- LWR in an assembly to assembly basis I.

or in a much more detailed pattern of channels (i.e., combining lumped channels outside of the hot assembly with a fine mesh of I

subchannel inside of the hot assembly, that will allow the analysis I

of the whole core in only one run. It has the same capabilities as the Input presentation described in Appendix 3.8.2, except for I area and gap variations that were deleted because of their small use in LWR, plus some others such as the printing of the images of I

each card immediately after it is read, the possibility of giving the power per node as input data, the use of coupling coefficients I

in the mixing term of the energy equation and a new model (i.e., the I Baroczy model) to calculate the two-phase friction factor. For I

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I these reasons we strongly recommend the use of this option in the cases described above.

I This option is described in Appendix 12.

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CHAPTER 4 I

DESCRIPTION OF THE ORGANIZATION OF THE CODE I AND OF ITS NEW SUBROUTINES 4.0 Introduction I

The organization of COBRA IIIC consists of a very long *1 MAIN routine which combines several functions, namely (a) Read Input Data, (b) Print Input Data, (c} Initialize Variables, I (d) Control Hydraulic Calculation, and (e) Print Results. The organization of COBRA IIIC/MIT is more.complex because MAIN was I

split in order to distribute the functions listed above among several subroutines. Also, due to the new Input Data Presenta-tion and the new capabilities incorporated to the code, some I new subroutines were required.

The objective of the present chapter is to describe the I

organization of the code in order to facilitate an understanding of the program in cases where it is desired to incorporate some I

new improvement. Also, in the last part of the Chapter the I description of the task that each new subroutine executes is given.

I 4.1 Organization of the COBRA IIIC/MIT Code I The new MAIN is very short, only 7 statements, and its only task is to guide the calculations. It successively calls INDAT I

(i.e. to read in Input Data) INPRIN (i.e. to print Input Data)

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I I I and CALC (i.e. to start the hydraulic calculations). From CALC I itself a call is made to EXPRIN which prints out the results and returns the control of the code to MAIN to start a new I cycle in cases where more than one case is analyzed.

In Figures 9, 10 and 11, the order in which the successive I subroutines are being called is given. These figures will be I of great help in the understanding of the following description.

4.1.1 Read in the Input Data I As said in Section 3.8, there are two options to Input the I Data, one when NGROUP is equal to 20 (new Input Data Presenta-tion) and the other when NGROUP takes successive values of 1

.I through 12 (original COBRA IIIC Input Data Presentation). The last one uses subroutine CARDSl to read in card group number 1 I (i.e. physical properties of the coolant) while the remaining I of the Input Data is read from subroutine INDAT except when IPILE =1 or 2 (analysis of PWRs or BWRs in an assembly to I assembly basis) at which time card group number 4 (i.e., descrip-tion of channels and rods) is read in from subroutine CARDS4.

I Subroutine INDAT initializes also all the variables that require such initialization.

I From Figure 11 it can be seen that some other subroutines I are called from INDAT in order to fix the dimensions of the arrays and to determine the array LOCA (which is done in subrou-I time ACOL).

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When card group 20 is selected (Figure 10) the new Input I Data Presentation has to be used. In this case, subroutine INDAT initializes the variables, reads in control cards Cl, I

C2, C3 and C4 and makes a call to subroutine CORE to establish I the dimension of the arrays. Then the control is transferred to subroutine CARD 20 which reads in cards defining the mapping I of channels and the average heat flux (i.e. cards C5, C6, C7 and C8). Subroutine READIN is call~d from CARD 20 to read in the I

axial and radial peaking factors (i.e. cards C9 and ClO) and I CARD 20 itself reads in the number of axial steps and time steps (i.e. Card Cll). Then the control is transferred to subroutine I ITHO which calls successively to subroutines CHAN, MODEL, OPERA, FIZPRP and TABLES which read in respectively the description of I

the channels and the rods (i.e. Cards from Tl to T7), the hydrau-I lic model (i.e. cards from TB to Tl9), the steady state and transient conditions, inlet enthalpy, mass flow at the inlet I and outlet pressure (i.e. cards from T20 to T25a). Now subroutine FIZPRP will calculate the physical properties of the coolant I

making successive calls to HAPROP, HLIQ, HVAP, ROLIQ, ROVAP, SATTEM, and SURTEN. Finally, subroutine TABLES identifies the channels, I

rods and nodes for which final results are to be printed (i.e. I cards from T26 to T30). The control returns again to ITHO which calls to CORE 3 to check whether or not enough storage was given I to solve the problem and prints the size of those variables whose size is problem dependent. The control is then transferred again I

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I I I to OPERA, CHAN, MODEL and FIZPRP successively to print out the I Input Data and the physical properties of the coolant.

the reading of the Input Data is ended, a call is made to Once I PRECAL to establish the initial conditions.

I 4.1.2 Print the Input Data When the reading of the Input Data is ended, control is I transferred to INPRIN via MAIN to print out, if desired, the Input Data. The printing is selected with variable Nl (card C4).

I If card group 20 is chosen, the printing of the Input Data I described here can be skipped since a similar print out was already obtained.

I 4.1.3 Thermal/Hydraulic Calculations I The scheme used in COBRA IIIC/MIT is the same as that used in COBRA IIIC. First, CALC (part of the old MAIN) establishes I the boundary conditions for the steady state problem and starts an iteration loop which sweeps the calculation through the core.

I Subroutine SCHEME is called in each iteration to perform the I calculation for every axial step. Mass flow convergence is checked at the end of each axial step and when all values are I inside the convergence factor the calculations are ended. Other-wise a new iteration is performed.

I For the transient calculation, the steps described above I are performed for every time step until the end of the transient is reached.

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4.1.4 Print Out of the Results I

Once the calculations are ended, subroutine EXPRIN is I

called from CALC, which will print out the results. Several options are available in the INPUT DATA to allow for the selec- I tion of results which are desired to print. Once the printing is over, the control of the program is transferred to MAIN I

which calls to INDAT to start a new case if there is one. Other-I wise the program stops.

4.2 Description of Subroutines I

Several of the subroutines used in COBRA IIIC/MIT are new, some as consequences of the new features incorporated into the I

program, and others because of the different organization of I the code. The rest of the subroutines remain almost unchanged with only small modifications to allow for the introduction of I

the new features.

is given.

Here the description of the new subroutines I

4.2.1 MAIN I

The new MAIN guides the calculation: I INIT =1 I

2 CALL INDAT (INIT, NOPRIN)

IF (NOPRIN. EQ.O) CALL INPRIN I

CALL CALC (which calls EXPRIN)

I INIT =2 GO TO 2 I END I

I I' I First a call to INDAT is made that will read in the Input Data I and initiate the variables. After this step is executed, a call to INPRIN is made to print out the Input Data only if I NOPRIN in Card C4 is set equal to zero. Then CALC is called to do the hydraulic calculations and CALC itself will call EXPRIN I to print out the results. The control returns then to MAIN I which after making INIT = 2, in a new case if there is one.

will call again to INDAT to read Otherwise INDAT will stop the I program.

(' 4.2.2 INDAT If card group 20 in card C4 is not called, either the origi-I nal or the simplified Input Data Presentation (which combines card groups 4, 7 and 8 in only one) are used. This subroutine I then, as explained in 4.1.1,"will read in the Input Data. But I if card group 20 is called, INDAT will only read in the four first cards and then will call subroutines which pript as well I as read Input Data. In ari.'y case, INDAT initiates the variables.

INDAT has cards from MAIN 5365 to MAIN 8830 of the old MAIN.

I 4.2.3 INPRIN I As indicated before, this subroutine is only called when NOPRIN is set to zero, and then will print out the Input Data I in the same fashion that COBRA IIIC does. INPRIN has cards I from MADI 8840 -to MAIN 0350 of the old lVl..AIN.

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4.2.4 CALC I

This subroutine performs the hydraulic calculations. CALC I has the cards that in the old MAIN were named MAIN 0360 through MAIN 1820 and from MAIN 2340 through MAIN 2405. I 4.2.5 EXPRIN I With this subroutine, the output is printed and has cards from MAIN 1822 through MAIN 2331 of the old MAIN. I 4.2.6 CARD 20 I This subroutine is called from INDAT where card group 20 is selected. Its purpose is to read and set the following data: I a) b)

The channel map, i.e., the array NTHBOX (I,J).

Channel powers, i.e., the average heat flux AFLUX:

I' the axial heat flux profile NAX, Y( ), AXIAL( ); I the radial power DATA (ZRADIA+I).

c) Channel length (z) and number of axial intervals (NDX). I d) Total time of transient (TTIME) and number of time intervals (NDT).

I This information is passed to ITHO via the argument list and COMMON. I 4.2.7 ITHO I

This subroutine is called from Card 20. Its purpose is to control the Input Data reading and printing. It calls CHAN, I MODEL, OPERA, FIZPRP, TABLES to read in Input Data. It theh calls OPERA, CHAN, MODEL, FIZPRP again to print out the Input.

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I I I 4.2.8 CHAN I This subroutine is similar to CARDS4. It reads the channels and rod parameters (e.g., area, grids, rod diameters, etc.) for I various types of channels and specifies which channels are of which type.

I 4.2:9 MODEL I This subroutine sets the hydraulic model. A preset model is I obtained by submitting a blank card representing a number of indicators all set to ZERO. Alternatively, various parts of the I model may be changed by setting individual indicators of non-ZERO. For example, the mixing might be preset to S = 0.0~ if I Nl = 0 but changed by setting Nl = 1 and giving an extra card with a new value of S. Correlations for two-phase friction, I subcooled void, slip ratio may be preset but changed if required.

I 4.2.10 OPERA I Th~s subroutine sets the operating conditions, for example mass velocity, transient forcing functions, etc.

I 4,2.11 FIZPRP I This subroutine sets the physical properties. By giving a blank card, values would be calculated automatically to span I the problem range.

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4.2.12 TABLES I

This subroutine reads in and sets the variables which control I the channels, rods, and nodes that will be printed on EXPRIN.

I 4.2.13 READIN This is an auxiliary subroutine for reading in certain I quantities within a DO Loop.

I 4.2.14 TIDY Its purpose is to set variables which are used when printing I 0

but not during the hydraulic calculations. It is only entered if NOPRIN = O, i.e., if the original COBRA IIIC printing (in I

INPRIN) is required in addition to that controlled by ITHO. I 4.2.15 PRECAL Its purpose is to set certain variables which would otherwise I

be set in INPRIN in preparation for the hydraulic calculation I (e.g., the flow split at inlet). PRECAL wa~ written as a separate subroutine in order to keep intact the other Input Data route I via INDAT and INPRIN.

I 4.2.16 CARDS 1 Its purpose is to read from cards or calculate from polynomials I

the elements of the physical property arrays. It is called from I

INDAT when NGROUP =1 and it calls to HLIQ, HVAP, ROLIQ, ROVAP, SATTEM, HAPROP and SURTEN successively when Nl < O to calculate I the physical properties from polynomials.

I.

I

I I I 4.2.17 CARDS 4 I Its purpose is to read and process channel, grid and rod data when Card Group 20 is not chosen and IPILE = 1 or 2, in I other words when the simplified version of the original Input Data, which combines card groups 4, 7, and 8 in only one, is I used.

I It is called from INDAT when NGROUP =4 and IPILE = 1 or 2 and it calls to ACOL to set array LOCA for use in setting up I cross-flow matrix.

I 4.2.18 CORE This subroutine is described in full detail in 3.2.4. It I computes the origins within the DATA ARRAY of the old, fixed arrays A, NTYPE, etc.

I 4.2.19 SEPRAT I This subroutine is described in 3,5,3.4. It contains the bulk of the modifications required for BWR assemlby to assemlby I calculations.

I 4.2.20 QPR 3 I Its purpose is to read in QF and QC, fuel and coolant heat generation rates for each model volume. For more details see I 3. 6.

I 4.2.21 ACOL This subroutine sets the LOCA ARRAY. It is called either I'

I

I I

from INDAT, CARDS4, or CHAN depending on the Input Data presenta-I tion being used. This subroutine is described in full detail I in 3.1.3.

4.2.22 BAROC I

This subroutine is described in 3.4.2. It calculates the I two-phase friction pressure drop following the Baroczy correla-tion. I 4.2.23 SURTEN This subroutine calculates the Surface Tension (lb/ft). .,

I 4.2.24 HAPROP This subroutine calculates Liquid Specific Heat (Btu/lg °F), I Liquid Viscosity (lb/ft hr) and Liquid Conductivity (Btu/ft 2hr °F).

I 4.2.25 Functions ROLIQ, ROVAP, HLIQ, HVAP and SATTEM Their function is to calculate Liquid Density (lb/ft3), Vapor I Density (lb/ft3), Liquid Enthalpy (Btu/lb), Vapor Enthalpy (Btu/lb) and Saturation Temperature (°F), respectively.

I The subroutines described above are those which are new in I

COBRA IIIC/MIT with respect to COBRA IIIC. The rest of the subroutines used in the MIT version of COBRA are basically I

unchanged with respect to COBRA IIIC and only small modifica- I tions have been incorporated in some to reflect the introduction of new subroutines in the overall code. These modifications I were described in Chapter 3.

I I

I I

I CHAPTER 5 PRESENTATION OF RESULTS I

5.0 Introduction I It is the intention of this chapter to show two different I points, first that both codes, COBRA IIIC and COBRA IIIC/MIT, yield identical results when applied to the same problem and I second to present the new capabilities of the code with respect to Input Data Presentation and running time. To prove the I first point we had to select a case which fit within the restric-tions of COBRA IIIC. A case with only 10 cahnnels and 13 rods I was chosen. To show as much as possible of the second point, I the 10 channel by 13 rod case was arranged into a rather rare pattern of channels and rods (Figure 12). The representation I of Figure 12 can be vi~ualized as a reactor core in which channel 7 is an actual subchannel while the rest of the channels repre-I sent lumping of subchannels.

I Three different runs were made of this sample problem, one with COBRA IIIC, one with COBRA IIIC/MIT using the same Input I Data Presentation as before, and the final one with COBRA IIIC/MIT using the new Input Data Presentation. The results and conclusions I are presented below.

I 5.1 COBRA IIIC In Appendix 13 the listing of the cards required to be inputed I in order to describe the problem, and the results obtained, are I given. The case, like the two following, were run on the IBM 370/168 computer at MIT and in Table 11 their cost is given.

I

I I

5.2 COBRA IIIC/MIT With the Old Inout Data Presentation I As can be seen by comparing Appendix 14 with 13, the results obtained are identical, except for some values of the I

D.N.B. Ratio, to those given by COBRA IIIC. The slight difference I

in the D.N.B. R value is due to the fact that in COBRA IIIC/MIT the effect of the spacers upon th~~ll-:F.EL_.is taken into account in the W-3 I correlation by taking TDC=0.019 as recommended in reference 18 where-as in COBRA IIIC the parameter TDC is taken as zero.

__ I 5.3 COBRA IIIC/MIT With the New Inout Data Presentation I From the listing of the cards required to describe the problem, (Appendix 15), it is clear that the reduction in I

Input Cards is quite substantial when this option of inputing I the data is selected. Also, from Appendix 15 it can.be conclud-ed that the results are almost identical to those of the pre- I vious cases, the slight differences being due to variations in the physical properties of the coolant between their calculation I

from polymonial expressions, in this case versus cases 5.1 and 5.2 I

where they are inputed.

I I

I I

I I

I I I CHAPTER 6 LISTING OF THE COBRA IIIC/MIT CODE I

The listing of the code is given in Appendix 18 in I the following order:

• I 1. BLOCK DATA 17. GAUSS 33. ROVAP 49. PHNTIM

2. AREA 18. HA PROP 34. s 50. CHF I 3. BAROC 19. HCOOL 35. SATTEM 51. CHF2 I 4.

5.

BVOID CALC

20. HEAT

21. HLIQ

36. SCHEME

37. SCQUAL

52. DIFFER

53. DIVERT I 6. CARDSl 22. HVAP 38. SE PRAT 54. IND AT

7. CARD20 23. INPRIN 39. SOLVE 55. MODEL I 8. CHFl 24. ITHO 40. SPLIT 56. TABLES I 9. CIJ

10. CURVE

25. MAIN

26. MIX

41. SUR TEN

42. TEMP

57. ZIGET

58. ZIFREE I 11. DE COMP 27. OPERA 43. TIDY

12. DOY 28. PRECAL 44. VOID I 13. ELAP 29. PROP 45. ACOL

14. EXPRIN 30. QRP3 46. CARDS4 I 15. FIZPRP 31. READ IN 47. CHAN I 16. FORCE 32. RO LIQ 48. CORE I

I I

I

I I

I References

1. "MEKIN: MIT-EPRI Nuclear Reactor Core Kinetic Code", CCM-1, I

R. Bowring; J. Stewart; R. Shober; R. Sims.

2. D. S. Rowe. "COBRA IIIC: A digital computer program for I

steady state and transient thermal hydraulic analysis of rod bundle nuclear fuel elements." BNWL-1695 (1973). I

3. K. Hansen. Personal Communication.

4. R. W. Bowring. "Simplified Input Data for COBRA IIIC when used for PWR and BWR Cases". MEK-20 (1974).

I

5. J. W. Stewart. "MEKIN Data Management". MEK-9 (August 1974). I

6. R. W. Bowring. "An Introduction to COBRA IIIC Coding". MEK-~O (November 197 4) .

I

7. R. W. Bowring. "COBRA IIIC Modifications to Subdivide MAIN".

MEK-36 (April 1975).

8. R. W. Bowring. "The coding for a Faster COBRA IIIC Cross-Flow I

Soluti.on". MEK-28 (January 1975).

9. R. W. Bowring. "Timing Runs for the Original and Modified I

COBRA IIIC". MEK-31 (January 1975).

10. S. L. Smith, "Void Fractions in two-phase flow; a correlation I based upon an equal velocity head model", Proc. I.M.E. Vol. 1, Pt. 1, No. 38, page 647, 1969-70.

11. C. J. Baroczy. rr A sy_stematic *correlation for two-phase pressure I

drop".. AICHE-ASME H.T. Conf., Los Angeles, Aug. 1965, 12.

Preprint 37.

I J. H. Keenan, F. G. Keyes, P. G. Hill and Joan G. Moore. "Steam 13.

Tables". pub. John Wiley and Sons (1969).

Electrical Research Association. "1967 Steam Charts".

I St. Martins Press, N.Y. (1968). Pub.

14. I J. R. S. Thom, W. M. Walker, T. A. Fallon and G. F. Reising.

"Boiling in subcooled water during flow up heated tubes or anriuli". Proc. Inst. Mech. Meg., Vol. 180 IIIC, p. 225 (1965-6).

I

15. W. H. Jens and P. A. Lattes, ANL4627 (1951).

I

I I

I 16. J. C. Chen. "A Correlation for boiling heat transfer to saturated fluids in convective flow 11

• ASME Paper 63-HT-34 (1963).

I 17. F. W. Dittus and L. M. K. Boelter, Univ. California Publs.

Eng. ~' 44, (1930).

I 18. J. Weisman and R. Bowring. "Methods for Detailed Thermal and Hydraulic Analysis of Water-Cooled Reactors".

I Nuclear Science and Engineering 57, 255-276 (1975).

I I

I I

I I

I I

I I

I I

I

I I

I I

1 1 2 2 3 3 4 I

4 6 7 I

5 8 6 7 10 8 I 11 I

2 13 11..I I

9 1 10 1 11 1 12 I 8 19 20 I I

13 2 14 23 15 21..i 16 I

I Figure 1.

I Channel and Boundary Numbering Scheme I

I I.

I

I I

I I ..... l I 1 2 I  ; J 3

I '+"""' 4

/ ~5 5 9 r

I 3 i

6 o,_ c.9 J

}1 8 10 1

I l3J 9

"'12 I '-l I+ l 5..r*

"'l 6 I 11 ,..., l ., 12 13

.-1 8 I

I I

Figure 2. Channel and Boundary Numbering Scheme I

I I

I I

I I

I

/

I

/

A B c /D

/

A B c y' E F C?f c E F c{ c I

/

/

/

/

H J: F B H /I F B 1... 'J"

/

H E A 4

/

H E A I J H E A NC = 10 NC = 16 H I F B I c

E F G I

A B c D NG = 32 I I.

D c B A A B c D D c B A A B c D c G F E E F G c c G F E E F G c I B

A F

E I

H H

J H

J I

H F

E B

A B

A F

E I

H H

J H

J I

H F

E B

A I

A E H J J H E A A E H J J H E A I N

c F

G F I H E

H E

I F

F G

B c

B c

F I H H I F B I

G F E E F G c D c B A A B c D D c B A A B c D

~

I

---

NC = 64 I

NC = 128 Channel Layout for 10 to 128-channel cases. All channels I

Figure 3.

were identical except for their radial power factors which were arranged symmetrically as indicated by letters A-J. I.

I

I I I IlE:\T THA:--:SFEH.-LOS A:--!GELES C!IE~!IC,\L E.:\GI:\EE!n\G l'IWGIU:ss SY~!POSit\l ~EiW*:~

I I

I ~

Q)

/MJO +---"'<--'< --<.---------4----------+-----------j 1

!CC.0

..-l 0...

i I µ

..-l

~

l J

I c::

0

• r-i

µ u

• r-i I 11.

~

I

,oL I I I I 0.1 I

I SOOIUM ("fl FREON-22 (°Fl 1200 1400 1600 1800 200J 40 so ea iOO 140 POTASSIUM ("Fl 1000 1200 1600 1eoo 2CCO AUfllOiUM (*FJIOOOL.-----'1200~---14..,.00,,.---1""'eo~o--:1@00 I

,. _. MERCURY ("Fl ~-------'~-----,0C0.._..

600 __""'.'.12~00~--'."14CO WATER ("F) 212 328 .. 67

_ Figure 4. Baroczy Two-Phase ?riction l1ul tip lier I at G = 1.0 Mlb/£t 2 hr.

I

I 16 I

1$

,.. I 13

.... I LZ

..*o-l.

2:

cl

• I.I OS

.I I

I I

I I

I 09 I

I I

0.6 o~oLooi-------------:-~~oo~,------------~oto~*-------------:.0~1--------------

PROPERTY INDEX, l1'1ll'vf*~l'ZI'* I I

Figure 5. Baroczy Mass Velocity Correction to Two-Phas~

I Friction Multiplier I

I I

I

> I I s I 4

'3 I :,.~.::.

~ .  !

Polynomial Experimental I

I """""

H c...

(!)..

c...

I ><

Cl)

"i:::I c::

I H

+.)

""'Cl)

I 0..

0 0...

I I

I

/rJ'tJ .2~ Jao .Soa /cr;a I

Pressure (psia)

I I

I Figure 6. Physical Property Index (PPI) vs. Pressure PPI = (µL/µg)0.2/(pL/pg)

I I

I

I I

I I

ic o o u .

• _ _ . . - - - - - - - , - - - -

1Quality %

~----------- -----

- ;C c'I I

I Ii I

-:*~-c-1 I

i...

Cl)

~

~

I

+.l

-~

j

~

i::

0

+J u

i

• ll~

I

• .-! i

-~

i...

Cl) i I

Ul -

______3 ! L:_

~

..c::

0..

I

--- I I

I l' I 0

3

"

E-<

! I 1---------4---------~-"--==========+:::::===~~~.1 I I a.0001 o.ool a. a I o.; I I

Figure 7.

I Baroczy Two-Phase Friction Multiplier at G = 1.0 Mlb/ft 2hr. I CODE VALUES (Plotted by computer from subroutine BAROC) 1-1

I I '-

-100-I /. 'S I-~

I /. 3

i. "Z.

I /.I

/, 0 c.q I o.~ 0 (J,7 I (I., ."J CJ.5 I a.;,

o.ccc.

I /. 8 I /.1 J. i, ~

'"'J

~-*.?J..17 '{ (t.)

~

I ;5

/,J.,

~

~-

\

I ~1

/.3

.z "

/.I """

I /, 0

\

~)

-ac:

/J. <1 I 0-~

• ~

.( l o-7 I "* ~

o-5 o.coal a ..:01 o.cr 0.1 Figure 8. Baroczy Mass Velocity Correction to Two-Phase Friction Multipliers CODE VALUES (Plotted by computer from subroutine BAROC)

I

I

-101-I INDAT - (Read in the INPUT DATA, see Figures 10 and 11)

I INPRIN I

FORCE AREA I QPR3 PROP- HCOOL Only for the first VOID axial station I

MAIN PROP BAROC VOID

-E CQUAL BAROC HEAT - TEMP - GAUSS I

MIX SCHEME ---...+-DIFFER (Enthalpy Increase) I CALC- FORCE AREA I PROP- HCOOL BVOID I.

VOID- SCQUAL_

t BAROC I

DIFFER (Pressure Drop without Crossflows)

SEPRAT I

DIVERl~~~OMP 1soLVE I DIFFER (Mass Flow Increase)

-DIFFER (Pressure Drop with Crossflows)

SE PRAT I

I EXPRIN - CHF - CHFl or CHF2 I

Figure 9. Organization of COBRA IIIC/MIT I

I.

I

I -102-I I CORE - ZIGET CHAN ACOL CORE2 I INDAT -

DOY TOD READ IN MODEL OPERA HAPROP HLIQ FIZPRP HVAP I CARD20 ITHO TABLES ROLIQ CORE3 ROVAP I OPERA CHAN SATTEM SURTEN I TIDY MODEL FIZPRP

[HAPROP SUR TEN I

PRECAL

--f PROP CURVE I SPLIT I

I I

Figure 10. Organization of the Reading of the Data I When Card Group 20 is Selected I

I I

I I

I

I

-103-I CORE - ZIGET DOY I

IND AT ---+-TOD HAPROP

• I CARDSl - [

SURTE~-[J CARDS4 - ACOL - CORE2 (if IPILE 1,2) I CORE3 ACOL - CORE2 CORE3 I

PROP CURVE I

SPLIT I

I I

I I

Figure 11. Organi-zation of the Reading of the Data When Card Group 20 is Not Selected I I

I I

I I

I

I

-104-I I

I I

I s I 5 J I 8 I "8" I l 0 I 10 I

I Channel: 5 Rod: 5 I

I Figure 12. Arrangement of Channels anq Rods in the Example Problem I

I I

I

I

-105- I I

COST($)

CASE SIZE STORAGE READING CALCULATIONS PRINTING I 101 Channels 500K . 25 22.09 8.53 I 101 Rods I

30 Channels 30 Rods 275K .16 6.51 3,34 I I

10 Channels 10 Rods 210K .10 1. 08 1.83 I

I I

11 I

Comparison of Storage Requirements and Costs With Problem Size Using COBRA I'IIC/MIT on an IBM 370/168 I TABLE 1 I I

I I.

I

~*

I

-106-I I

I K LOCA (K,L), L = 1, 8 I 1 2

l 2

4

-1

-2 5

-5

-3 0

-6 0

0 0

0 4

5 I 3 3 -2 6 -7 0 0 0 4 4 4 1 -8 -11 0 0 0 4 I 5 5 -1 2 8 -9 -12 0 6 6

I 6 7

6

'7 I

-2

-3 3

10 9

-14

-10 0

-13 0

0 0 4 I 8 ,. 8 -4 11 5 -9 -12 0 6 9 9 -5 -8 12 6 13 7 I

I etc.

I I

I LOCA Array for Case of Figure 1 I  ;

TABLE 2 I

I I

I

I

-107-I I

K = 1, 14 LOCA(K,L), L I

1 1 2 -3 0 0 0 0 0 0 0 0 0 0 3 2 2 1 4 6 9 -13 15 0 0 0 0 9 I

3 4

3 -1 4 14 5 -16 0 0 0 0 6 9 15 0 0 0

0 0

0 0

0 0

4 I

2 9 5 5 4 6 7 9 13 15 3 -16 0 0 0 10 I 6 6 4 5 7 9 13 15 -8 0 0 0 0 9 7 7 4 5 +6 9 13 15 -10 0 0 0 0 9 I I

I I

I LOCA Array for Case of Figure 2 TABLE 3 I I

I I

I I

I

I

-108-I NC 10 16 32 193.

I NK 12 24 52 356 I Steady State (Iteration) Seconds I Cross-Flow Rest .

0.31 0.21

1. 73 0.39 15.02 1.21 -

I Transient (7 Iterations)

Cross-Flow 2.31 12.64 105.42 -

I '

Rest 1. 01 2.48 7.84 -

I Calculated (per Iteration)

I Cross-Flow 0.33 1.80 15.07 3274 Rest 0.15 0.35 1.16 13 I

I Notes: Averaged and Calculated Times are for 10 axial intervals and per hydraulic iteration. All results with H Compiler.

NC=l93 represents extrapolation to PWR but values should be doubled for 20 axial intervals.

I Calculated values from Cross-Flow: *t = 0.08 + 0.000235(NK) 2

• 8 I Rest: t = 0.0027(NC)l.75 I

I ,

Timing for Original COBRA IIIC (10 Axial Intervals)

TABLE 4 I

I I

I

I

-109-I NC 10 16 32 64 128 193 I

NK 12 24 52 112 232 356 I MS 11 15 15 31 63 59 Stead;y State ( 1 Iteration) Seconds I

Cross-Flow Rest 0.06 0.11 0.10 0.21 0.27 0.41 1.37 0.77 9.16 1.59 I

i l Transient (7 Iterations) I

n. Cro.ss-Flow 0.32 0.81 1.95 9.65 63.09 -

l Rest 0.71 1.12 2.51 4.19 8.35 - I Average(per Iteration)

I Cross-Flow 0.05 0.11 0.28 1.38 9.03 -

Rest 0.10 0.17 0.37 0.62 1.24 - I.

Calculated(per Iteration)

Cross-Flow 0.05 0.12 0.28 1.38 9.05 12.99 Rest 0.10 0.16 0.32 o.64 1.28 1.93 1 Notes: Average and Calculated Times are for 10 axial intervals and. per hydraulic iteration. All results with H compiler.

I NC=l93 represents extrapolation to PWR but values should be doubled for 20 axial intervals. I Calculated values from:

Cross-Flow: 2 t = 0.00282NK + 0.00000837NK*MS + 0.0000127NK 2 I Rest: t = O.OlNC I

Timing With New Cross-Flow and New "Rest" Subroutines (10 Axial Intervals)

• I TABLE 5 I

I

I

-110-I I

I I No. Channels 16 32 64 128 I Previous Values Cross-Flow 0.11 0.28 1. 38 9.03 I Rest 0.17 0.37 0.62 1.24 I Total 0.28 0.65 2.00 10.27 I New Values Cross-Flow 0.13 0.32 1. 51 9.27 I Rest 0.19 0.36 0.71 1.39 I Total 0.32 0.68 2.22 10.66 I Increase in Running Time 14% 5% 11% 4%

I Notes: "Previous Values" are taken from the Average Values in I Table 5.

The "New Values" are directly comparable and are given I for (a) the solution of the cross-flow equations and (b) the rest of the Hydraulic calculation.

I Running Times per Iteration - in seconds I TABLE 5A I

I

Two-phase multiplier

[For G = lx106 lb/(hr.)(sq.ft.)]

0 Property index

. Quality, (%)

~~)/(:~)

0.1 0.5 1 2 3.5 7.5 10 15 20 30 40 60 100

. 5 80 0.0001 2.20 5.80 9.20 16.0 26.5 47.0 99.0 163. 376. 630 1,300 2,050 4,300 6,600 10,000 0.001 2.15 5.60 8.80 14.8 22.8 34.2 48.2 70.0 108 1118 240 330 538 760 1,000 0.0011 2.08 4.90 7.80 11.9 16.3 22.8 29.0 36.0 49.5 63.0 86.o 110 155 203 250 0.01 1.59 3.30 11. 80 7.00 9.60 12.4 16.o 20.0 27.0 33.5 43.5 53.0 69.0 85.0 100 0.03 1.12 1.55 1.81 2.57 3.115 4.7 6.10 7.90 11.0 13.2 17.3 21.2 26.0 30.0 33.3 0.1 1.04 1.12 L22 1.48 1. 78 2.05 2.50 2.80 3.60 4.20 5.50 6.50 8.00 9.10 10.0 0.3 1.01 1.02 1.06 1.13 1.26 1.36 1.50 1.59 1. 77 1.93 2.25 2.48 2.86 3.20 3.33 For a property index equal to 1, all two-phase multipliers have a value of 1.

I I-'

I-'

I-'

I Coordinates of Two-Phase Pressure Drop Correlation TABLE 6

p T µg µL l/pg l/pL PPI psia oF io-6 lb/ft.sec ft 3;1b Prop. Cale. Error %

211. 97 240 8.23 160.0 16.327 0.0169 0.00187 .00175 -9.3 119. 2 280 8.73 134.o 8.650 0.0773 0.00345 .00324 -6.2 117.9 340 9,55 104.24 3,792 0.0179 0.00761 .00741 -2.7 247.i 400 10.42 87 .111 . 1.866 0.0186 0.01524 .01526 0.1 466.3 460 11.18 75 .116 0.9961 0.0196 0.02892 .02885 -0.2 7113. 5 510 12.01 67,73 0.6153 0.0207 0.04765 .04723 -0.9 1002 545 12.61 60.38 0. 41149 0.0216 0.06641 .06640 0.0 1225 570 13.61 59,58 0.3537 0.0224 0.08509 .08518 +O.l 1541 600 14.28 56.80 0.2677 0.0236 0.1162 .1160 -0.2 1784 620 14.87 52.94 0 .. 2209 0.02117 0.1441 .143'7 *-0.3 2057 640 16.05 119.58 0.1805 0.0259 0.1798 .1808 +0.6 2529 670 18.06 43.95 0.1278 0.0288 0.2692 .2683 -0.3 2892 690 20.58 35.04 0.09113 0.0325 0.3833 ,3901 +l. 7 "Prop II ** PPI = (µL/µg)0.2/(pL/pg)

"Cale": PPI from polynomial I

I-'

I-'

f\)

I Comparison of Actual ~nd Calculated Values of PPI rrABLE 7

-113-I I

x I

n

% PPI=0.0001 0.001 0.004 0.01 0.03 0.1 0.3 I 0.1 307 0.980 0.788 0.743 0.813 0.796 0.827 0.5 1.

1. 442 1. 015. 0.785 0.712 0.773 0.827 0.923 I 1 1. 543 1. 054 0.782 0.710 0.805 0.819 0.839 2 1. 662 1.094 0.800 0.718 0.778 0.766 0.793 I 3.5 1. 781 1.141 0.833 0.731 0.774 0.748 0.723 5

7.5

1. 796

1. 785 1.136 1.178 0.814 0.844 0.723 0.730 0.729 0.719 0.737 0.714 0.700 o.678 I

10 15 1.790

1. 731 1.161

'1.177 0.853 0.863 0.719 0.707 o.678 0.627 0.721 0.680 o.684 0.679 I

20 1. 719 1.190 0.864 0.695 0.614 0.610 0.672 30

~-

1. 695 1.188 0.893 0.705 0.579 0.610 0.636 I 40 1-730 1.212 0.902 0.705 0.525 0.576 0.625 60 1.652 1.215 0.941 0.738 0.517 0.537 0.595 I 80 1.862 1.231 0.938 0.739 0.502 0.522 0.472 I

I I

I I

Value of n in M = 1-X + Xn/PPI I TABLE 8 I

I I

CORRECTION FACTOR AT PPI =

x 0.00026 0.00380 0.05700 0.19800 0.00026 0.00380 0.05700 0.19800 0.00026 0.00380 0.05700 0.19800 G = 0.25 MLB/SQFT. HR G = 0.50 MLB/SQFT. HR G = 1.00 MLB/SQFT. HR 0.001 1.669 1.160 1.220 1.110 1.300 1.130 1.100 1.078 1.000 1.000 1.000 1.000 0.010 1.669 1.158 1. 307 1.166 1.330 1.250 1.15() 1.086 1.000 1.000 1.000 1.000 0.035 1. 626 1. 059 1.355 1.420 1. 311 1.170 1.150 1.232 1.000 1.000 1.000 1.000 0.050 1.600 1.000 1.384 1. 572 1.300 1.120 1.214 1.320 1.000 1.000 1.000 1.000 0.075 1.590 1.210 1.502 1. 695 1. 300 1.148 1.210 1.334 1.000 1.000 1.000 1.000 0.100 1.580 1.420 1.360 1.818 1.300 1. 276 1.219 1.460 1.000 1.000 1.000 1.000 0.150 l.580 1. /120 1.360 1.818 1.304 1. 256 1. 223 1.472 1.000 1.000 1.000 1.000 0.200 1.580 1.420 1.360 1.818 1.308 1. 236 1.240 1.596 1. 000 1.000 1.000 1.000 0.300 1.534 1. 324 1.330 1. 619 1. 284 1.195 1.235 1.457 1.000 1.000 1.000 1.000 0.400 1.492 1.234 1.340 1.445 1.260 1.153 1.230 1.318 1.000 1.000 1.000 1.000 0.600 1.362 1.139 1.162 1.204 1. 200 1.110 1.130 1.164 1.000 1.000 1.000 1.000 0.800 1.178 1.103 1.086 1. 070 1.100 i.070 1.084 1.061 1.000 1.000 1. 000 1.000 CORRECTION FACTOR AT PPI =

x 0.0026 0.00380 0.05700 0.19800 0.0026 0.00380 0.05700 0.19800 G = 2.00 MLB/SQFT. HR G = 3.00 MLB/SQFT. HR 0.001 0. 750 0.864 0. 905 0.970 0.630 0. 780 0.865 0.9J7 0.010 o. 740 0.660 o. 880 0.912 0.610 0.484 0.810 0.884 0.035 0. 749 1. 676 1. 829 0.817 0.625 0.501 0. 741 0.769 0.050 0. 75!1 0.686 o. 798 0.760 0.634 0.512 0. 700 0. 700 0.075 0.752 o. 704 0.805 0. 730 0.634 0.551 0. 701 0.671 0.100 0. 750 0. 721 0.812 o. 700 0.634 0.590 0.702 0.642 0.150 0.736 0.746 0.788 0.665 0.606 0.605 0.673 0.587

o. 200 0. 722 0.750 o. 764 0.630 0.598 0.620 0.643 0.540 0.300 0. 746 0.788 0.730 0.602 0.624 0.667 0.593 O.l193 0.400 o. 770 0.806 0.696 0.574 0.650 0. 714 0. 5112 0.454 0.600 0.820 0.860 0.705 0.574 o. 718 0.782 0.542 0.454 0.800 0.910 o. 932 0.820 0. 700 0.836 0.880 0.690 0.580 Values of the Mass Velocity Correction Factor for In~erpolation Between in Figure 9 TABLE 9

I

-115-I MASS VELOCITY MLB/SQFT. HR QUALITY o.o 0.25 a.so 1.00 2.00 3.00 1000.00 I PRESSURE = 500.0 PSIA (PPI = 0. 0310) o.o 0.001 0.010 1.000 1.347 2.270 1.000 1.347 2.270

1. 000 1.236 2.090 1.000 1.117 1.782 1.000 1.000 1.480 1.000 0.944 1.313 1.000 1.000 1.000 I

0.035 4.350 4.350 3. 898 3.376 2.683 2.319 1.000 0.050 0.075 5.940 8.525 5.940 8.525 5.460 7.099 4.577 5.936 .

3.537 4.643 3.010 3.961 1.000 1.000 I

0.100 10.517 10. 517 . 9.432 7.657 6.061 5.182 1.000 0.150 0.200 0.300 14.624 17.544 22.256 14.624 17.544 22.256 13.101 15.827 20.536 10.648

12. 773 16.751 8.290

9. 719 12.447 7.003 8.147 10.212 1.000 1.000 1.000 I

Q.400 0.600 0.800 26.999 29.117

31. 647 26.999 29.117

31. 647

24. 877 28.329 31.386 20.514 25.170

29. 039 14.785 18.622 24.543

11. 912 15.001 21.278 1.000 1.000 1.000 I

1. 000 32.262 32.262 32.262 32.262 32.262 32. 262 1.000 PRESSURE = 1000.0 PSIA (PPI = 0.0662) I o.o -*l. 000 1.000 1.000 - 1.000 1.000 1.000 1.000 0.001 0.010

o. 035 1.277

1. 735 2.942 1.277 2.942 1.161

1. 735 -* 1.537 2.504 1.058 1.345 2.159 0.966 1.189

1. 786 0.925 1.102

1. 607 1.000 1.000 1.000 I

0.050 3.690 3.690 3.218 2.623 2.081 1.836 1.000 0.075 0.100

5. 020 5.477 5.020 5.477 4.031 4.830 3.291 3.870 2.619 3.090 2 .295 2.689 LOOO 1.000 I

0.150 7 .292 7.292 6.457 5.153 3. 984 3.414 1.000 0.200 0.300 0.400

8. 630 10.973 13.058 8.630 10.973 7.823 10.144 6.098

8. 039 4.560 5.745 3.845 4.670 1.000 LOOO I

13. 058 11. 976 9.653 6.576 5.130 1.000 0.600 0.800 1.000

13. 905 14.804 15.096

13. 905 14.804 15.096

13. 512.

14.765 15.096

11. 914 13.656 15.096 8.211

11. 000 15.096 6.311 9.241 15.096 1.000 1.000 1.000 I

o.o 1.000 1.000 PRESSURE = 2250.0 PSIA (PPI = 0. 2121) 1.000 1.000 1.000 1.000 1.000 I

0.001 1.123 1.123 1.091 1.016 o. 986 0.954 1.000 0.010 0.035 0.050 1.266

1. 915 2.322 1.266

1. 915 2.322 1.182

1. 671

1. 964 1.092 1.372 1.510 1.001 1.135 1.169 0.971 1.072 1.082 1.000 1.000 1.000 I

0.075 2.837 2.837 2.254 1. 716 1.280 1.183 0.100 0.150 3.267 3.796 3.267 3.796 2.648 3.100 1.851 2.150 1.329 1.474.

'L226 1.314 1.000 1.000 1.000 I

0.200 4.238 4.238 3.738 2.400 1.566 1.361 1.000 0.300 0.400 0.600 4.607 4.680

4. 665 4.607 4.680 4.164 4.285 4.518 2.915 3.299 1.825

1. 977 1.523

1. 601 1.000 1.000 I 4.665 3.914 2.346 1. 900 1.000 0.800 1.000 4.724

4. 716

4. 724

4. 716 4.687 4.716 4.430

4. 716 3.182

4. 716 2.679

4. 716 1.000 1.000 I Multiplier Arrays at Various Pressures I TABLE 10 I

I I -116-I

~

READING OF PRINTING OF INPUT CARDS CALCULATIONS INPUT AND I E OUTPUT I COBRA IIIC 0.20 7.17 5.68 I COBRA IIIC/MIT (Old Input Data 0.20 3.27 5,83 Pres.enta t~_on)

I COBRA IIIC/MIT 6.50(l)

I (New Input Data Presentation) 0.08 3,38 I (1) In this case, two print outs of the Input Data were obtained, while in fact, one is enough.

I I

I I

Comparison Between Costs of COBRA IIIC and COBRA IJIC/MIT I for the Problem of Figure 12 TABLE 11 I

I I

I I

J I

I

-117-I I

APPENDIX 1 I

Subroutines ACOL, DIVERT, DE COMP and SOLVE I

I I

I I

I I

I I

I I

I I

I

I -118-

~ IJ ~ o 0 UT I 1\! F: ll C 0 L ( TF ~ 0 '-1

• p<

• J K , KM A X , L0 C A' ~A

• MS , N K , ~ G

• I P I LE )

Ir<<1l .JK(ll *L'.)C~("Ar..,ll I* nr'<'IFNSinN ACOL

("

.c-SET LOC!* n~FI~I~G I~Tf04CTING BOUNO~~IES r~on~

L0Cal~*ll=<.

= 1, CALLEQ F~OM CA~OS4, LOCAC><,Ll*L=2*7 SPECIFIES UP TO

~OtJ"i[JA,.;iit:S llO.JAC=:"H TO \,-IAN\IELS OEF"I~I"JG BOUNOA~Y ~ *

=

J '1 ,.. ><: l ' ,.., -<

= 2. FqOM MAIN COLD CO~PA)

LOCA(~,8)

IP (rcru::.GT.f)) GO T'.1 1117 I D') 103 L=2*13 tn3 LOC6. (~.L) ='1 r:.O TO 110 I 107 DO 3L=2,7 1 LOC.1(><',U=n lJ. 0 .. j : 1 LOC A ( K, l) = r<

I* II JJ

= IKIK>

= JK(Kl

.:.. 00 7 t<.r<= 1 ':>..JI<:

II III = IKIK:><l IF (!II.GT.fl> GO Tt/ 7 JJJ = JK (!-<'<)

! F ( < I I

• 1

• I I Il

• 0 P

• c !I

• E ~

• J .J J > l 3 0 T0 6 I ~

GO TO 7 IF ( (I!l+JJJ - II-JJ) .::a. Ol GO TO 7 N = l\J+ l I LL IF

= IT I (I!.E!).III> LL=JJJ

~v = FLOAT<II-Lll/FLOATCII-JJ)

I LOCA (K .~Jl = ~K IF (wV.LT.().0) U1CA(K,N)=-K:-<

7 C'>"JT rr. uE1 IF !I~ILE:.GT.f') ina I LOCA (K

• l~l =~1 Gt') TO 109 GO TO 1 *1 ;; L*) <: A ( "<

• R l =\J I l!iq IF (II .GF:.JJl Gn TO B rr = JK ( r< i J:J = !K(Kl I ,:; ("

GO TO c0 ~.JT Il'JU t...

_ ~r~n STRIPE WIOT~ FOR AAA MATRIX I~ )!VERT I NIAX =0

!)0 10 K:l,\JK I* N=LOCA(K'.tRl IF (!iJILE.GT.Ql

~!=LO C ~ ( < , l t. l GO TO 111 111 n0 10 L=2*'l I L~L = !A8S(L~CA(~*L>l J = IA~S P<-Ll(L)

IF" (J.LT.M!iXJ GO TO 10

=

I 10

-1AX KMA)C =K CONT I l\iUE J

MS = 2*MAX + 1 I C~LL RE TUR'!

COOE21MS,NKl E!-lO I

I SIJ=lPOUTT~ff IJTVF'Qr(Jl

-119- ,,

c r-irs  ;:ioor.i:::D1J;:lF' cn~HA It\!<:; r~:: COWA()N ANIJ TYPE STATE'-"El\ITS c;L4AR~D SY THEnVRTl'IO,.

c '-' A J () P SU 8 ~ 0 U T Pl i::: S () F" C 0 ~ o a. - l I I C *

• r') V~ T f"l 0' ,

c c

T>.i o L I C I T I T Er; f. q COMMQr-i /C()~PAl/

( 'S M~ETA l

.~FLJX. .ATOTA~,8FIETA *DIA .DT ,ox I l ~LEV ,F'E~Pn~.FLO .~T~ .Ge *GK .G~ID .HSURF tHF

• 1 t.

~Fr; J3

,1-1r,

• . J4 NAFACT,N4~AMP,NAX

.r2*

,J5

.!3

,J6

,\JAXL oIERRl')~,IQP3

,J7

.N88C

• ITER~T,Jl tKOE'3UGtKF' tNCHAN oNCHF tNOX ti<LJ tJ2 tNF I

c:; "IGAP5 *"J(";P!IJ oNGP!f'lT,\JGTYPEtNGX,L *NK *NODE~ tN011ESF'tNPROP ,

~

7 NRAMP .NPOD .NSCRi. .\JV QA1 .~~OF" .RHOG ,SIG~A oSL

,NVISC~tOI tTF

,PITCM ,POWER ,PREF tTFLUTDtTH~TA ,THICK

, I

~ 11F ,llF' .VFG ,VG ,7 c

C0*.4vQN ICOQPD.::>/ AA(t...}

• AF(7}

• AFACT(lOtlO>

• AV(7)

• AXIALCJO},

~XLC10). 8~(4}. 8XC3fll* CC(4), Ci.~AD<2l, CFUELC2l* nFUF'LC2l*

2 GACYL(l!il* GF'AC_T(qol(lle G~If)XL(lnlt HGAOC2l* HH'°(30l* HHl;(3Q),

1 4

TGPto(ln). 1<CLtOC?l. -<FtJELC2lt Kl(=-('3QJ, "ICH<lOlt Nc;Ap(oJ, PPC)f)). OCL~.!)(2) .~F' 1 .JF:L(2) .ssIGMA(30)' TCLA0(2)' UUF'(30)'

I 5 VVF(JOl. l/VGC'30l, :t.n11AL(30l, YC30l

• TTC30) c c

LOGICAL GC!D I

Pf::AL KTJ, KF* KKF, KCLAO, KFUEL c

c I.

COMMON 1coqPAJ1 ~a .~c ,MG *~N .MR ,Ms .~x ,.

1 l

i 1iDHOX

~~~

'SCC!-!d~I. q;r,'.)

.~f')HYn tiA

• ~CHF';:;;

,$AAA

• $CO\J

,$QHYf)~,1.£0IST o$AC t'SALPHA,'§AN

• $COND , SCP * $0

,$OPDX ,;;QPK: ,'§OUR

,$ANSW~t$8

, $1')C

,$nR

, 'liOF"DX

• SF I

1 ~FACTO,~F'OIV o5FI~L~.$FL0X ,$FMULT*iFOL~ ,~FSP ,$F'SPLT*~FXFLO*

4 c;

~GAP .~~APM

~!f)FllE.~IiJGAP.'bIK

.~GAP~ .iH ,$HFIL~*~HINLE*IHOLn

.~Ji3'.1!L,'fiJK *SLC

,$HPERI,~InARE,

• SLEN'3TtSLOCA tSLP ,

I

~ ~MC~F~.~MC~~C.iMCF'C~.~NTYP~.$NWRd~o$NWRPS,$P ,$O~~IM*'liPH ,

7

~

q

~PHI

<<;QUlll

~u

.~P01'.JTC.~PQ"ITR.~PR'ITN,$Pl.al

,q:;:)A(')TA.~PHO

.~u;.i

,5RHOOL,$SP

.iU5AVi;::.'5USfAP,$V t'SPWRF ,$QC

• ST

.svrsc

,$QF'

,$VTSC:\IJ9$VP 9 115QPRJ~,

.':llTOUMY,$TTNLE,'STROD ,

tSVPA

• I A ~w .~woi_n ,$WP .~~SAVE.$X t'SXCROS c

COMMON 0AT4(})

I Ll1G!CAL*LOAT!ll PHEGEq IrH TC 1 l Et:l U TVAL El'J C E <I) AT A ( 1 l , I n A T ( l l , L DAT ( 1 > >

c I,

c A8ITCIZ.z1.z2,73,z4,z5,z6l = rz~<(2.0*Zl - Z2 + Dx/0Tl/Z3 +

l Z4*ABS<ZS+7-6>*0Xl

!PILE =J7 c

"-!Kl< = "'IK JMl = J-1 SLOX = SL~l)X.

DTGC = f)T~~r.r.

DXGC = DX*GC C C4LCl.JL~TF. USTAR

I -120-I no c:; K= 1 .1'!'<!<

t !=!OAT (~tJ.<:+o<J 1")VRT040C i)VRT04lr:

JJ=IDAT('liJ'<+Kl r")VQT()42C I c::; CONT I NUF.:

=

0 A T A ( '5 I J S A 1/ c:- + '< J f) A T A ( <li I J c; T '1 ~ + "\ l I) AT A ( ';IJ 5 TA ::i + i<) = 11

• S* ( IJ J\ TA (SU+ I T l +DAT A ( liU +JJ J l r')VqT 043 i l)VRT044i i)V'H045C c

I c SF:T AAA AOOAY IJSTNG LnCA <SET IN ACrr_. BASED LMA x = :~s ON p~ouT DATA)

'*l!IJ = ("4S+ll/2 I D0 ~ l O ~ = 1

• 1'1 :<

,, ?911

[)') ~90 L=l *L*'-1A:t OATA(5AAA+K*~K*(l-ll I T=IDAT ($!!<+;<)

JJ=TOAT(~J~+:-<J l=0.

OATAl~8+KJ:(0ATA(~SP+K+~*G*(J-lll-(OATA($0PDX+IIl-nATAl$0POX+JJ)J* nVRT064C l OXl*Sl*~ATA(~FACTn+~l*OATA<~USAV~*~J*OATA(~W+~+MG*(JMl-lJJ/ nVRT064l I*  ? DXGC*OATA(~W~LO+K+M~*<J-l)J/OTGC SAVi:=ABIT(l .OATj,($1..J*ITl .JATA($USTAR+"\J ,QATA($A+!Il .DATA($('1Pl<+!Tl, i)VRT0651 r)VRT065C 1 0 A T '1 ( ~ F

• T T + 1..1 C * ( JM l - l l J , 0 A T A ( 'Ii F + I ! + MC * ( J - l ) ) )  :")VRT0652

+AB I T ( 1 ~ 0 AT A < 'f lJ +J. J J * ) AT A ( <;; IJ ST Ai:l * -<: I

• 11 AT A ( 3 A* J J l , 0 AT A ( $I") PK +.J J ) , r)VRT06S:3 I :2 1

IF <IOILE.GT.l)J GO TO OAT~(~F*JJ+MC*(J~l-llJ.QATAliF+JJ+MC*(J-lllJ 7~13 r)VRT065<-

N80UNO=!DAT(~LOCA*l<'.+~r,013J I* GO TO 7214 7213 NROUND=IDAT!~l0CA+K+MG*7) 7214 DO 300LL=l.11.1:;011~JI')

I l =!DAT<~L0CA+~+~G* (Ll-ll IF ILL.F.:0.1> GO TO 29C::

IZ = 1 l

II=" <L.LT.n> !7=-1 I l TJ

=

=

IABS<Ll JJ IF< <I.!.EO.T!):H(<=;IK'+ll l .'.)R.

I 1 l

<II.E0.I~AT(~JK+Llll SAVE = ABIT<I?.DATA C<iill+TJJ ,QATA(SUSTA.~+Ll ,QATA('1iA+IJJ

• IJ=II DATA (<i;l')OK+IJl ,QATA (<t;r+IJ+MC*(JMl-lJ l ,DATA ($F+TJ+MC*<J-ll J)

~qc; L = MI n - K'

• L I 300 OATA(~AAA*~*~K 0 <L-lll=S~VE 0 SLDX/GCOOATA(~FACTO*K)

OATA(~AAA+~*~KO(YI0-1l I=

lOATA($AAA+i<'*NKOC~ID-lll+Sl*C!J(KoJ)o)ATA(SFACTO*Kl+

I* 20ATA(~USTAO+~l/OXGC*l.IDTGC 310 Cf')NTINIJE IF < J 6. LT. l l GO T n l IJ S nVRl'.0670

!1VRT06<:;lQ c

I' DVRT0700 c MOl')!FY SIMULTANEO!JS EOUATin~s TO ACCOUNT FOR SPECIFIFD VALUE<:; OF l)VRT0710 c,.. CQ 0 S SF l 0 1:J r; I V~ 1\1 I ~I i::; UP i:i nI JT T ~ E ~ 0 PC E DVRT0720

'- rJVRT0730 00 go 1<=l*'lt< OVRT0740 IF<LDATC~FiJIV+~)) GO rn '10 DO P 5 l = l *  !"'.

LL=MIO-K*L I IF(LL.EQ.MT~J GO TO g~

IF< LL. GT. L1.411 X. nq. LL.LT. 1 l GO TO 85 IFCLDAT(5Fi)IV*Lll I l l

85 CONTINUE 0ATA(5W+l+MG*(J-l))

DATA(!8+~l=OATA(~3*~l-0ATA(~AAA*K*NK*lll-1J l*

OVRT0790 911 CONT PJU!:

I 1)0 100 K=l.NK DVRT0800 f"JVRT0810

-121- I tF(.'JOT.LilH(:lii='l')T\/*l<'.l l nn gs L=l *LoAA'/.

30 TO 100 .I i i'JATA(~AAA*><'*'.Jt<*~(L-lll = oJ.O LL= tw1AX0(1.(l+K-1*:1(1)ll i_L=M!llJfl <LL.~-'<)

MOICU=M!0*"'-Ll.

I g~ f) A TA ( ;: ~A A *LI_ +Ni<* ( MD I CI_ 1- 1 l l =0 * (1 0 AT A ( ~A A A+ I'( * ~*lK '-> ( M r ')- l l ) = l

• 0 OATA(5R*Kl=~ATA(~~*~*~Go(J-1Jl ion CONTI NU~

1r)5 IF (l<OE~IJG.L T.] l :;o rn l 1 !')

PP. I ~-J T 2 * ( < n A T A C:;; A A A + k' + l'\J <: ~ ( L - 1 l l , l =1 , L ~A X l , DA T A ( $ ~ + K l

• K =l , *'I K K )

2 F"l')RMAT(lHI). lP7F="l5.L..) .

l l () CALL r.lF.:("IJ~O(\i~e!FPPO~*LMAX,*"1ID*DATA(liAAA+ll ,OATA(~:\NSIME*ll, l . 0ATA($3*1> *i\JK)

IF<!ERPnR.r;r.11 GO TO 1()00 CALL SOLVE(N><',L'-1AX.~*qn.nATA('SA4A+ll ,JATA('bANS'.NE+l} .DATA($i:l+l) ,NI<}

rJO 150 K=l.~ll<K 150 ()AT A ( 51.i

• K+ 1.1 G* ( J-1 l l :DAT A ( .ii~ \IS \v F. +..:; l p i:rr_JR "J 1011() PP.! "lT 1 1 F(")0MAT(2L..~ i='QonR IN i'Ji='Cnv.P, DIVE~T IF.:C(PQP =3 P.;:TURN E: f\JI')

I I

I I

I I

I I

I -122-I 5 tJ RP. 0 l )T I i*J f n I "-1f:1'J<::; r ON n E c nM 0 ( N "'

• p::* :.i R 0 R ' L ..., Ax * '-1 I ) ' lJ L

• x

• R ' NK )

! IL ( j\Jf(. l ) * 'i ( 1 l * ~ ( l l

,g c SIMPLIFIED vEoc:;tON OF" 4 R ~ 4 Y 8 EC 0 *AF" S ( i< * ( M I i) - :.< + Ll QF":O~O S T () ;::;> E f) ! AG '11\1 ti. L 8 M*I (1 0 'r 6 AA '-' AT q I x

• WITH ~n

) Tt\J "J 'n'

?!VOTING

i 0 S I T I 0 N P< , l l

<1 ~ q AY

• I N S QI I AP E

,~

l\J = ~*Jl\J DC0Mf'l060

- !F(l-J.E~.ll PFTUR".1 IC NM!

iJO l 7

= l\J-1

~ = 1* N~.q DC0~0290 DCOMOJOO PIVnT = ULf~ .~tnl

• 1 KPl = K+l LIMIT = "I>.Jn (N. C'<"+MI*1-l) no 16 T = ~PloL!~IT OC0M0460 l<K' = .*.qn+k'-!

'I* f:M = -1.JL ( ! *"'"<) /P!VOT

!IL ( T ,t<i<) = -::M IF (E~"l 20.l~.~'1 OCOMOSlO 2n 00 21 J:KPl*lIYTT I JI=t..A!f)-! +J JK = MTG-K*J 21 IJL CI oJ ! l = I Jl CT, JI) + f-*..ti>IJL ( K.JK l I* c 1 f:> CIJ"lTI NUE 17 cor-n I NtJE OCOM0570 OCOMOS80 I IF 18 PC INT 112 100 P~P.IT 113*

(UL ("-I *MT[)) ) l Cl , l8*l9 CCllL(-<'.,L),L=l*NN>,K=l*NNl DCOM0610 DCOM0620 111 FQPMATC7~1~.A) DC0!'-40630 I 112 FOPMAT(S~Hn<::;I~~UL4P.

!E 0 qop = l/

Mt.TOIX IN nECOMPJSE. ZERO DIVIDE IN SOLVE. l!')COM0640 DCOM0630 l Cl PETtJ~!'J DC0M0660 I E"ID r)COl-10670 I

1*

I I

I I

I

I

-123-slJ 8 c 0 u T *p~ i: c; 0 L I I F:: P*l "' ' L M <l 'I.

• M El ' u'-

• x

• R

• Ii r ~EN s r 0 l\j ! IL ( "1 k"

• 1 ) * ;( ( l ) * ~ ( l )

\j "( )

I c o<.u c

STOCE IJIAG(11\IAL ;:i1.1'JI') 0'" AAA "iATPIX.

AP.PAY i=!ECO*"'ES (K'. ("!!i)-o<+L) l Ii\J l\JE:""

~.J = !\JN*

~oc;rTIOl\l A~RAY.

p~ SQlJAQF.:

I c;OLVn0'30 I F' ( *,1

• F Q

• l l Ci 0 TI') S NPl = ~~*l SOLVoo**

c SOLVOO~

X(ll = 8(1>

rJ o 2 r. = 2 * ~,, ~oLvnol

!~l = I-1 SOLVOlf 5U~ = O.O 50LV0110 JM!N: MA.Xl'l(l.(!-M!l)+ll l .

C IJOIJBLE PRECI5!1')1'1 MAY 8E Pf'.:'QJiREO FOR !N"ER LOOP. SOLVOll 00 1 J = JMTl\Jo!Ml JJ = ~Il)-I*..J

= SI.JM UL< T. JJ)

• X LJ l l SUM

? x <I l

+

= 8 < ! l - c;1 I'"

SOLV0160 I

XC"ll = X(l\J) /Ul.(NoMT'"ll 00 4 !BACK = 2*"1 i;OLVOll I = MPl-I8AC;( SOLV0200 C I GIJE'S C~l-1 l * ***

• l 50LV02j

!Pl = I+l SOLV02

~UM = O.O c;OLV02" C DOllALE Pl=ilECISJ<11\J MAY 8E: l:IS::IJJIRED F"OR IN\JER LOOP. SOLV02SO

=

J~AX DO JJ

~INn(N.(!+MID-ll 3 J = rct.JMAX

= MIO-I*J l

I 1 SUM= SUM ... UL(!.JJl*X(Jl 4 X<tl = (X(Tl-5UMl/UL(!,,,,.IDl Ri:"T1.1;:<~.1 c;OLV021*

s x(l ) = 8 ( l ) /UL ( l

• M l:r))

P.F'.TUPN E"JO SOLV031 I

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-124-I I APPENDIX 2 I Input Data for 32-Channel Case I

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COf.'.IT*1ENT CARDS HAVE BEm.J ADDED FOR GREATER CLARITY, I

THEY ARE NOT IJ:. TCLUDED nr THE I:'JPUT DATA.

2000 I

1 1 0 CARD GROUP PWR NC=32 STRIPE BOU~TDARY HUMBERIHG 1 (FLUID PROPERTY POLY. OPTIOH)

I 1

1

-1 1000.0 2600.0 30

• I 0 CARD GROUP 2 I

2 1 0 0 0 0.184 -0.2 I 0 CARD GROUP 3 O.D 3 21 0.144 0.050.309 0.100.783 I

0.151.050 0.201.280

0. 251. 45 o.*3oi.54 0,551,40 o.351.59 o.4oi.6o 0.451.56 0.501.50 I.

0.601.28 0.651.14 0.700.95 0,750,775 0.800.588 0.900.312 0

0.850.450 0.950.200 1.000.094 CARD GROUP L!. 7. 8 (SIMPLIFIED P~{R DATA PFE.SE:TTAT!ON)

I 1

1 32 7

1. 0 3 4 37.43 1 0 348.o 1

310.2 0 .122 o. o 0.374 265.0 I

4. 0110

• 9 7 80

• 5 5 5 l.1281.1521.1521.0581.0901.1651.1821.1521.0031.1641 *

• 1651.1521.0631.0031.0901.123

1. 06 31. 00 31. 0901. 12 81. 00 31. 16 41.1651, 1521. 0901. 1651.

1821.1521.1281.1521.1521.168 0.05 1.16 2.32 3.49 3.66 3.87 2.99 1 4 8 2.0 .08 640 ** 3228 8.80 .076405.0.02241000.

c CARD GROUP 9 9 1 1 0

.5 0. 144. 0. 10 1 1. 20 c CARD GROUP 10 10 1 0 0 1 0.02

I -126-I I c 11 CARD GROUP 1

11 1 2 2 2 2 I 2250.

o.o 1. 0 557.3

1. 1. 056 2.66 0.189 o.o 1. 0 1.1.15 I 0.1.000 0.1.000

1. 0.77 1.1.000 c CARD GROUP 12 I 12 132 3 2 2 3 132 I 1 4 5 I

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t 1*

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-127-I I. I Appendix 3 Timing !Iethod I I:

1*

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• 1*

• t

• 1 I

I

I -128-

• a I Successive calls to the nei:*r. subroutine PP1J':1Ir.T (r:t) -

I coding in Appendix 16 - were made from i1AI~r and SCHEI7E in COBTI.A IIIC, as tabulated below.

I IN Called from After Card Description I --0 Ml'\IN (old 1304 Def ore outer DO Loop on time steps

'I -1 2

MAIN (old M.'\IN (old) 1306 1610 Within and at start of DO Loop on tiMr. st-

~;ithin and at start of DO Loop en i terc:i. tic I

,. 3 4

SCHEME SCHEME 0482 1080 Within and at start of DO Loop on axial steps Irn.r.lediately before CALL DIVERT 5 SCHEME 1090 Immediately after return f=oM DIVERT

• • 6 7

MAIN (old)

MAIN (old) 1650 1730 Immediately after return fr on SCHEME Just after end of DO Loop on iteration I 8 MAIN (old) 2360 Just after end of DO Loop on tin~ steps I The calculation followed the sequence.

0: Start timing run I 1: Start steady state calculation

• 1 2: Start first iteration over whole channel

3. Start interval calculation to set inlet conditions I

,. 3:

4-5:*

Start interval calculation for first interval Solve cross-flow equations (3,4,5): interval calculations for successive a.:<ial steps I 6: return to MAIN having completed first channel iteration PRINT RESULTS FROM PRNTIM I 2: Start next iteration 3-6: second iteration, as for first I

I

-129-1*

I PRIUT RESULTS FROM PrtlJTI::-1 (2-6): Successive iterations, PRIIJT Ii'Ror1 PR11TIM at each 6.

7: iteration closed Print COBRA output for steady state I

I 1:

(2-6):

Start transient calculation Successive iterations as above.

at each 6.

P?..PJT PROM PR:TTII1 7: iteration closed I print COBRA outout for transient 8: Calculation finished I PRIHT RE.SULTS FROM PRNTIM During each hydraulic iteration, i.e. 3-6, the total tine I

from the first 3 to 6 was stored and also the sumnation I of the times fror. each 4 to 5. Also the number of passes 3-3 and 4-5 were counted. At the close of each iteration I triggered by IN=6, the following were printed:

(a) the total time from 3 to 6 I

I (b) the summed time 4 to 5 (c) the lc..st times at TtThich stations () to 6 *;rere passed.

This informc..tion enabled the fo llmring to be deduced ~~d printed: I (1) time to solve the cross-flow equation, i.e. (b)

(2) time in rest of hydraulic calculations, i.e.

(a) - (b)

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I

I -130-I. (3) time for COBRA printing + time measurement printing =

I 1 (transient) - last 6 steady state) and 8 (final) - last 6 (transient)

I (4) and ( 2) above.

total time for run = 8 - O The results given in Tables 1 and 2 are (1)

The other results were used to check the I internal consistency of runs.

1 Load Modules: A symbolic source module was written with the dimensions given non-numerically, e.g. *&MC to represent the I number of channels; this can be seen in the COMMON list of I DIFFER in Appendix l:r..

I Two com.piled load modules, a "small" and a "large", were created from the source setting the array sizes through the Job I cards. The small module was used for the 10, 16 and 32 channel I cases and the large for the 64 and 128. A check run with 32 channels on the large load module showed that the running time I was not module dependent.

The load module dimensions are tabulated below.

I Symbol i.e Max. No. of Small Large t &MC Channels 32 130 I

,. &MA

&MG

&MN Array AAA Gap Connections Fuel Nodes 3136 56 10 15K 250 10 I &MR Rods Axial Intervals 32 31 1_30 31

&MX

I

-131-I' APPENDIX 4

1 Faster "Rest of Hydraulic Calculations" I II I

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I

.,, -132-I Subroutines DIFFER and HEAT were modified to speed-up the I hydraulic calculation - coding for DIFFER in Appendix 17, that for HEAT is relatively trivial.

DIFFER calculates for each channel, the local axial enthalpy I gradient DHDX, the flow gradient DFDX and the pressure gradient DPDX, without and with cross-flow. Each of these terms involves the summation of the effects of neighboring channels. In the original COBRA IIIC, the coding method was to use an outer DO Loop I on the channels and then, for each channel, scan every boundary in I turn in an inner DO Loop and to sum the effects. Determination of which boundaries were irrelevant required lengthy IF tests each time.

I The modifications to DIFFER consisted of using an outer DO Loop on the boundaries, assessing the interaction across the boundary

• 1 and then apportioning this appropriately between the two* channels concerned. With this technique there is no inner DO Loop and no I IF test to determine boundary relevancy. This gave a considerable I reduction in running time.

Care was taken when coding, to avoid adding successive small I* numbers to a large one with loss of accuracy due to round-off.

For example, in the enthalpy calculation, the small cross-flow,

'I mixing and conduction components are summed before being added to 1 the channel power. The COBRA answers obtained were identical in every respect to those obtained from an unmodified DIFFER - even to I' the last digit of the transient cross-flow.

I I

-133-I I

HEAT was also modified. This calculates the heat flux (FLUX) I and channel power from the rods (QPRIM). In the general case, several rods may heat a channel and the effect requires a DO I

Loop summation. H.owever, for PWRs and BWRs there is a one-to- I' one correspondence between rods and channels and the summation is superfluous. HEAT was modified by skipping the summation when I IPILE COBRA).

= 1 or 2 (i.e. PWR, BWR) but not when IPILE = O (normal I

The effect of the modification is to make a minute change in I the COBRA answers because of round-off. For example, by card HEAT0690, TFLUID is calculated as (0.0 + T*PHI)/PHI and this I

.can be different from T (the short-cut modification) due to round-off, particularly in the reactor case when PHI (the number I

of rods) is large, e.g. 264. The effect accumulates during the I calculation to give a detectable but barely significant difference in the COBRA answers. I I

• I I'

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I.

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I -134-I

1. APPENDIX 5 Subroutine Core and Block Data I

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1.

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I

-135-

<::: 1 J .:; :;; 0 U T T ** t: C;) ..; =

r*~ 0 1_r.::rr I':r=_:,-,,:::..;

I

(-5) r:::J~*'"')r*1  :) "'r.::. ( l l r: 0 ,*" "'} ~ 1 / c:-, ...J *::. ~ 3/ *.., ~ * *..j c , ,*;1 ,-; * *1 *\J , "" ~ * "" s

• M x * 'b s '£ , snR G < q 6 >

T*1Ti:1,;::.; ~I_ 'f ( .:;.; }

C 'l ~~ *~ *) ~;

,, ! '. f

• .:.iE~I i\j ~

FH IC r; ...Ju Q. .::; I S':t,*iE°S

• -::I\: AM f S

• 5 L X. , S T Y P ~

-~ T I :.; E ( :..; i;., }

(~;;)

I

'A;\

'*" ~ =

TF

l 1

( Wj

• L.:: * 'l ) ,\.11; =1 I

Ti="

~s-:::Y-':

• IJ l

(*~~!.L:.n) cn r =1 * <;;; ., s

'-1 \l=l I

1 rir1 x < I J :r.1c

.I

..i:.1_

<t LY. < 2 l :i)

~LX ( -'.-) =**:G

L .'f ( 7} ="'";

.;; I_ X (

<:'. !_ '( (

-;: :_ i I i

~ ) : ,~ ~

C'.) ='*! 1--: -=* c:;

~h1

1 ) : :*I,,;*~* '.1 ,(

X I

'=l_:fll2l=~r.

-1; i_ >'. ( 1 ... ) ='".;

-; 1_ x r 2 n J =:"i c ;:* ,... I

1_ 'i ( 23} ::"'\{]

~l_X

~l.

( 24) ::'1.:>

x r 25 l ::**1c ;:--.1 x I)

'hLX ( 2i:. l =*~G T

i::

f_ .< ( ;:'. 7 } : 1-.j (:,

L :t < 2 q l ='"1;::; ~:- "" X

1_ X ( 3 l)

MC;.'."IX I

<:: !_ .X ( J,... ) =Mr;'*' S

~L x ( 1:3 l

.;.1_ 't ( ],;., )

=~*1r;

=*-ir; I

Lx ( 37) =~*ir;-~*::..

I__( ( ] ,;: )

':. I_ '( I ::. l ):

=:*Ir:~:*~

-l:;t_ '.( ( ... .:.. ) =*-1;.;

,\.t !, *~* M

... '.(

X I

• *-;;1_ 't ( ~~)

-1_ x < 411 l ::"1r:

-;,1_:, ( 4>-:i l :MG

r11r, I

-.; I_ '( ( :+ *:) ) : M <:: -::* .:..

~l_X(50l=~G c;:l_X(5ll=MG'-l-l.:..

I

~LX <52J =*"IR'.l-6

~

• ~L:l

,_ x (5 3 ) =:wi ;(

<5.:..l =~t1X 1*

.::1_;r ( 55) :"-1.'.(

'ii_ X. ( 5q l =~-'C**"1X

• .:: L x < 6 2 l =.*P -;:. ,::..

-.::Lx ( 6t:.l :*.i..;i I

l3 l x ( 6 5 ) =,~: \l

<<:!_X. (67) :M(i:*"'1P

~L X ( t;~) ::'AC'.l-"'1X I

~l X ! (:;q) :i'"1CnA X

~L X ( 72 l

<<ii_:< ( 73) : '1(iHAX

=~-1 q 0

I

'5l X ( 74. l ::*"'lC*MX c

o<;l_.X ( 75J =*'-'1G'-'"'1X p 00 'I rn t: s;:; Ac E F"' 0:;; sp r ~.J 3 'fl R IT E c:;i AT r 0 \J

• I

I T:;' ( ; i_ ,I ( i :.: )

• LT * 'i:* ,.,, c) ~.1 x ( 7:; )

-136-

= 3 *Mr,

= .; . :

I  : !_

• -. ! - / (

f ( ., 7 :

7 .* j } = **1 :'.; *:~- :1 :.. -..:- . .tj "

= '

I

• !__ *' { *~ j ) ~

':"! * .( ( .:. 1 ) :: .:::

I  ::; '.(I

_'/ (".

,""' =

~,) = *!,.(

10~-~

5 ) -: :'. i:* *M* I I

':: I_ f { -:_

,,  :,."';:;*-: ( l) =l

.:::_, i 'i

-.r r.1_ f Jlr

'i :

=!j 7,1 i=*1 * .:::~~

.X i,, .. ;:.1. ~ ( T)

'. ~ ( T * <~ f

• l l  :>i

• 1:.;. () ( I l :: ; Ii,;) r; < I -1 ) + i L X < I -1 l I 1 1 :1

"'**" t:. y =1 I V ~-: ;(

~ ,:- ( "'*'.:.

s + "*' '}

.~

! I ( ,.""

• Li . ~L

+ l *2)

/, xl I lnn

~.':,.JD j\!\T,)("')

-i r) l ... :; t'

-<=i<::,,rn;;

= n.c,

,. ;= 1 * .., ;;; 5

!'. c;. :-:, { '** ) :: ~I).;(; ( *'i ) 5- 1 I

.. 'In <;: + K' r-

". ": T::; f c n ,.., ;: ._, ' **1 c ;:; * ~1 t\ o J I t-..:/. =~.ir:.. r-

? ) = 'f ...:.

I ~. l_ j (

c:;n:.;.,-; < ! J ;;,~,..,,-:.

..., I_ 'i x ='I I_ x ,'I, .. '

=

I_

(~-~ l *.1>L x ( o~ >

x (? )

r ~ ( ~- '*i.:. ~

• LT * *.; L;; X ) GO TO 902 I  ::l () ] ':. :*; j T ;:

c: T *'\ ::>

( *~ * -' i ; ij I )

• 1 r

.n? *' .:, r T *:::

c: T :~::

I -:.

• 3 Ii n :;l )

.*' f p y ( .'! .,. ,=- <

I

~

("

i:-::;n'" I,.,..,, .:-(,'-i Q.;;  ! '1T 1 P~G

,, _; TT :_ ( "-,

• l r, r, \ 1 )  :.1 i~ ' 1'<1 C * '-1 S * "1 N * '-1 ~ * ~ S ' "1 )(

., ,; T T::: ( ":, * '..-il r. !" ) (  :.J * *.:;1'1.t.. Mi:-.::; ( \j) ' -bl x ( f\j) '1i 0 ~ G ( l\j) ' s Ty p E ( N)

• N= 1 * $$Cl; )

I " ,;i r ,.. r:.* ( - * ) -} n r. )

I ,*1.,i::-~

.. : T 7 c:*

= ....

( ..,

• l *"'. r* ~ j v* '.A ti SL X 1.,

x

,**-~*!:'t_:il\T('<'14r..X-:<:o_XX)/1024.0

, 1_ 1*, .. ;  ::'. r<

I , ') _,., " >="...,::;, * *~ r ,/ / 1 * .1 '{ ~.j D. *i r r ., ;:.; )"( .:. Y s i zEs ' , / , ..1 A = ,* rs* / ,

~r = i~.  ;, ~~ = '* TS. /. ~N = I~. I.

I 1,

-=> ~. -

7

= ** l - * ' * \.., """ - '

• r s, /

• to~ A =' 9 r : :; ~

1'1".::.  :-".l 1/. J 1 *;.i*-1 IC C.T].::.i~r.:t: ~~;)IJI~En = '* Il4* l**OROS*, 11,

• ": i, 1 .*, , c. ! / ; , ) "i ..1 r: L r: t -< iJ co 1 JLG >i ll v :: 1 EE N RE: n.1 ! c En 8 Y * , r4* I( I )

• ,no.*

I -,nr:r; =--.,;*.,:--:'.,._ "*"'"'"*'f( l.\l_l_i)(;,~*rro-.~ ()F COP;::: 3JT 1i111iOOS*/)

<:11'\J  ;:-n:::*.1µ,T(t,j1)"'*IA*~irc Al_l_Ot:!lTI0~--J

-137-OF COO F"ATLED*///)

I 1 i) (\ ;;) ;:- *1 Q.;

I

. T I I ) ,") v.;

• • ii J'.**~C:;.:. '"F A *.1 [ c J. LI - I)\. :\ T I 0 *\j 0 F c 0 RE 3 0 T 0 NL y '

• I 1 () ' ' '*"Ci R !} 5 ' I u.)~1Jc:; .;lfr;11 i Ht:;:) F!lR T:-! rs PR0t3U:.'.M I'S ,

• I 10 I/ I) I

~an~ ~0cu~rc11)*.TJS.40J.*1=~~6Lt/TlS*40~. 1 2=INTEGEqt/T15*40X*'l=LOGTCAL 1 I//

.., r3:=;.

TJS.*-----

1 r*.:.~'f LE"'GTrl TYPEt/

---

*/

I

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I

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• 1 I

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I -138-T"AP!_Ir.IT r:.1rFr:.:'.~'~*4 Of:1'Ll:*,Q 31'-.!tiivl='.:~lq~)

n I "1 r:- \I<:: Tm) *: : L '( ( *::i .:. )

cou~oN ICQOCA~/ ~NA~~<::.~LXoSTYP~

f. IJ I JT V.~I_ E"* C;::: ( <t ~-! ~ *.1 F. <:: ( 1. l * <:: \J lv-1:: 1(l ) l * ( ~ \J A "'1F 5 ( 4 7) d 1\1A*.A:'.2 ( l ) )

oF~L'-'8 <;Nt.'.A~l (4i=,) /~i-JA o8rlAAA ,8HAC o8HALPHA

.AHCO I ]qHt~

?R'-irO~

1~HnHDX

.PHAN~~EQ

.RHC0N0

.R~OHY~

.~~3

.R~:~

ocH)~YJ~

oRHC:~ANL o8Hn

• ~HnIST

.RHOC

.RHnPOX o8H(HF~

,8HnFOX

.AHn?~

l._qµn,11;) .CIHf)q .qH=- *RHFllCTOR .RHFDIV ,8HFil\!LET '

I r::::;qµr:-r_ux

': q H!'i !I P

.;:i..;F*.1ULT

, .>:: -i *3 o. P '-J

.,,H;-OL'.)

• i*h~ 3 *A P c:;

.RHFSr='

• RHH

.RHFc:;Pt_IT

• 8 HHF I 1. "1

,AHIOGAO

.8HFXF"L('llri

, 8 H i..i I Nl F T a

7RYHl"'LO ,;:;,_,rl~E:)I,'IJI .'11-.i!DA~EA ,K:*iI)F'tJEL .8HTK I Pr:"AL*P 5~~~~2150)/

q~HJCOTL .~~JK ,Ri..iLC *8HL::'JGTH ,RHLOC~ .8HLR

• QqHMrHFP .~h~C~FRC .~~~CHFRR , Ri"fl-.Jf YDE ,8HNWRflO

• 8H~IWPAPS

• 1 I

• R.HPq I 1-.ITC .8HPR!NTq

!1,Ci-iO

• A-iPF~ '°'1 ,~H;>H ,EJHO-!l *

.c µpop.~ T~-1

• Ri..l.:>vn~F .8HQC ,8HQF , 8HQPP p.4 .

ci r:.c~t"'!l 141_

• P. HP'AI

,,.;.,qo.or AL ,HH~H() ,l:\HP-i00Lf) ,RHSP .8HT r)RHTf"1UIYIY * .;:i..;TI\JLET  ;;,,1..4TP()J .SHU .AHUH .8HtJSAVF '

I 0

r,9HU<:;T t.~ * .: , *-w .~!-iVISC

• FP-iV I sew ,8HVP e8HVPA

• FP,'-iw * .O.i-l*~;nL ;1 oRHllP oRHWSAVE ,8HXCPOSc:;

I'; CU-I~ * .c '"IR I

• t l T~TFGEP 31 ~q /

STY~f lq~) /7*1~2,l8*1*3*15*1*7*2*1*2*2*l*S*2*4*1*3*2*

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-139- I I

APPENDIX 6 I

Subroutine Ziget I I

I I

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I

I -140-I I. Subroutine ZIGET was developed at Savannah River Labor-atory to provide the capability for dynamic core allocation.

I The subroutine is written in assembly language and is restricted.

I to use on IBM Systems 360 and 370 computers. A listing of the assembly subroutine is included in this appendix. The use of I ZIGET is described below:

It is frequently desirable that the size of one or more I FORTRAN arrays be established at program execution time rather I than at program compile time.

directly support this facility.

The FORTRAN language does not However, an array can be

\I, dimensioned at length one and dynamically "extended" using ZIGET. The call to ZIGET is programmed as r:I CALL ZIGET(A(l), KMAX, LWORD,INCR,NPESRV,*)

I where A(l) = First element of the array to be dynamically allocated I KMAX = Number of words to be dynamically allocated I LWORD = Word-length of the array A (i.e. LWORD=4 means four-bytes per word).

INCR = Incremental address from A(l) to first word of the I NRESRV dynamically allocated area of core.

= Number of four-byte words to be reserved for other I uses.

= Error return I

Use of ZIGET is illustrated in the coding below:

I I

I.

-141- I I

C MAIN" PROGRAM I

DIMENSION A( 1)

READ(6,1000) KMAX LWORD=4 I NRESRV=lOOO CALL ZIGET(A(l), KMAX,LWORD,INCR,NRESRV,&901)

IF(INCR.LE.O) GO TO 902 DO 100 I=l,KMAX I

100 A(INCR+I)=O CALL ZIFREE(DATA(INCR),&903)

STOP I

901 Error stop. Failure in ZIGET.

902 903 Error stop. Not enough core.

Error stop. Failure in ZIFREE.

END I

I In the example above the call to ZIGET requests that KMAX I four-byte words be allocated to the array A. A minimum of

,~

1000 words will be reserved in core for other uses. If a fatal error occurs in ZIGET return is made to statement number 901.

If there is not enough core to satisfy the request, INCR is I

returned as a negative integer value and KMAX contains the I

number of words which are actually available. If the request for core can be satisfied, INCR is returned as a positive I integer address increment such that the Ith element of A can be addressed as A(INCR+I). (NB. FORTRAN statement 100.)

I Also illustrated is a call to entry point ZIFREE which I

deallocates the core previously allocated by ZIGET.

I I

I I

I -142-I C~LL !~*Jr, C~LL SE*-:itJE"C:E 7IGF:T CA.1'.lf)P.1.Lt"JGTH.I5U3.*l 'oir-IE~E A= ntlM"1Y nT.-1F""lc::;Tn1'1::D v'&OTA~t.E =-~OM CALLING PQQGCA"1 I i,ir, t M 5 = r 0 T .-. 1_ D r "' F" "1 c: r o:\j c; r 7 F. oi=- a.

• Lf~GT~ = L~~~TH c::;PF"~IFICATin~ F0~ FiqST ARGUMF"~T r C:IJR = P,1COF..:-AEr>.iT Al_ c::;J8SCP ror VAL JE ( FrJ~ l\JOR"'4Al RETURN l

• 1 l="QP C::CPO~ P~T! lq"!

ISlJR *= ** -AU. 'llJ<,4q:'.;.( OF ""O~QS AVAILA8LE I<:;Ug = _ogg, OY\JA"ATr STJCfAGE A~E~ NOT ACCES<:;IoLE I IF THF: *~~ONG l\JO.

PR!JGRAIA. A FC)RTqAf'.1 oi:- AP.GU"1ft\JTS T~AC::8ACK AP:: 0 ASSED FR0M THE CALI !l'\IG I<=i 3IVF:N (lHC230Tl I 7-TGF"T

!:? 11 r:Sf::CT l="Gi I I)

Rl i:-:~1 J 1 I CJ?

ql

iu

- :111

-Q!J

-'.)u 2

3 Re:  :::- *1ti c; I qk C7 i:-11; i:")lJ 7

Qq  ;:-Giu I oo Po\

qo c:-QU C::QIJ FQU 9

l l'l 11 P.r . C::QU 12 I Cf"\

ci:-

Qc:-

i=: ') t !

- '1! I C:-)f,I 13 l~

1 c:;

I Q cq q12 1 0.  :::"'JlJ C:-QU

(~lj 111 11 1?

R13 C:QIJ 11 I ~14 RlS i:" r) I.I C::~IJ l 'i i=lC ls.12c1c:;i I nc rJC SPA

'I. I 7 f CL7 1 ZTGET 1£.*12*12(13>

U=! 12. 15 I

q~ 15*15 I c::~

CiT U-1 7.7 7 .1_i:_:NriT"1 2.c;.r)Cll MIN!f'.AUM LOAD LENGiH AnJ~ESS OF ARGUMENTS T'-1 P<ll *X*8!i* TEST F"O~ COP~::cr NIJMR>:R nF APGS.

I t:'.NZ PPESET [F t:;.;d6CPll PIG~T NO. OF' APGc::;. 'gc:;i Al'ICH L

SLL Rk .,z-- c;ET VALUE IM ""::ms UNITS rlPEN (C::~1~PrJC~. (OIJTPl.tTl l FOP DEBUGGING Pucoos~

• ---------Gn GET ALL C~PE AVA!~A~LE

~Al r:? l 0

• Al_LG;:'.T

• --------MAKE SUP.F: CiYSTEM OVHi'l PEGlUF:ST IS J'.j A 2"\ 80lJ"l0Aqy LA ~k*20£.7<0,PAJ c::;pl P"ioll SLL q~*ll

-143- I

• ---------COMPUTE 5Y~T~~

L SP

=>::i.L~r,10.

~a. oi::,

nvE~~~AO I

C~JP A

ST RtT~~(")

c:;a.Anl')P qo,:>Fc::.\nf)

I ST ~i::,.qE~LGTH

• ---------~-~~ onn.o~- -o&-~~~~ ~-&&

8AL .? l 11, F;::;iE>:OVl.-ff)

I

• SNAP DC8=5~A~OCB.TG=0*5DATa=(C9> ,?QATA=QEGS nESU~G

• ---------CQMPUT~

RAL c:;T A~T

nn.R~TALL 1

n.O(Q*=>3l nF AO~A TO 9~ QETUR~~D TO USER I

• (S~!POC8l Puooos~

CLOSE P C\ITPL P,11="

FOR OERUGG!NG I

vvc !S1'J+2(2) *2fl4} PICK UP I\JTERl\JAL STATMENT NllMRER 1.* A l

l*PLT5T lCioI~l="R I

~.Al.~ ll.*15 APANC~ TO TRAC~8AC~ POUTINE PPESET ~QU I_

'~

7.11(3) LOAD Nn. OF WOPOS PEnUESTED.

I M

I PP 6.0(4)

7. 7 MULTIPLY 8Y LENGTH SD~CIFICATION.

R7= NUM3~R OF RYTES TO RF:QUEST

\I c;vE 5T 2.oEG:::>

LA 7.15(1'),7) * "!AKE SURE RF:~lJEST IS ON 8 8YTF: 80lJNOAPY SRL SLL 7.1 7.1 AND ADO 8 BYTES FOR CONTROL WORDS.

I ST 7.LENGT'-H:4 PEQUEST~D LENGTH (MAY)

C::PACE 1

• ---------FIQST. GET ALL AVA!LIA8LE aPEA

'3 A I_ R 1 0 , A l_f_ GET I

l.IJNTl FOU C

~~

~

• R7.LENA RtTR~Q COMPARE ~ET. LGTH WITH REQ, LGTH CALLER R~)UESTEO TOO MUCH. GO AnJUST I

SPACE 1

• ~- ------GET ::(t;l)UEST 6NTO TK 201J~IQAPY LA R7.2047(0.o7> I

<;RL R7.11 SLL

~T 07,11 R7.0PGLGTH

• ---------COMPUT~ SYST~M OV~P~EAO ACEA I

A R7,AOOC( COMPUTE ~ESERVE A9EA ST L

R7.RESA!)Q 97.LE~!!\

SAVE VALJE LOAO LGT~ OF A~EA 08TA!NEn I

R?.ORGLGTH SU8 LGTH ~F AREA 6ANT~O c:;

C CNH R7o7-EQO C'\JT=>LINF" CHECK Fn~ ~o SYSTEM A~~A AVAILIA8L5 IF' NOT, I.

ST cn.QSLGTl-l SP.ACE l

• ---------FO~E 5YSTEM 0VEPH~A~ AREA 8AL 01n.~~EEOVHD

<:;PACE l .

-ao-------:-SET UP CONTROL !NF()::lMATION INTO 03TA!NEO APEA C~TPLTNF ~QU ~

I L Ri::..AQOP GET AOOP OF CORE ALLOCATED MVC LA 0(8,~) .ADO~

"

• A ( 0 * .&, l

"""""'*'"""' 1*-

STORE CJNTP.OL WORDS AT 8EGIN~ING ADO 8 BYTES FOR CONT~OL WOROc;

~I l."""\t"'"',...rt. *r"\~

11',

I ..... -.. . . . . .......

-144-I c::T C::I:!

-S.PEGF-i:;. ;:i. 5UBTQGCT ADDRESS OF ~!RST AR~UµENT CIM ".:'~oo;i TF " E GA TI VE

• R E T1J Rl'\J I xR RAL

i1~.~1c; q l (I

• I) TI/

~ rI'JI51-!

I EPR()C i::'.PRliP 1

• AVC I_ A

~c

,, '"'*S) .;::cnnE lSe4(0*n>

l ":;. ~FT 1JOi'l PF.TUR~!

ERROR

'JOE-STORAGE ,._,r}T R~TURN (RF.TURN ll Ar,CESS IBLE FINIS!-' c:;T 7e0(0ei:;)

I LA

~

Q 1 l * ~ r F"=n:r:

~F:TUP.~1

<;P.ACF l I P~T~EQ

• ---------CALLER o

FUU

• qE~IJESTED Tnn MUCH CORE, PAc:;c:: RAC!<' VALIJI=" JF "1AX A~EA

~~EE OBTAINED AREA ANn Tr-IAT CAN 8E ORTAINED FREE"44PI V*A=AD.QP.<;c:O I LA L~

Ql~*"'

o 1 f1

• C" T11 1I 51-i SET EqP.n~ CODE l_ c"' .1_ F'. Ill .\

5 D"-

• 5Y5tWHn 5 ~~*EIGHT AO JUST FJ~ CONTRL INF"OQMATION 8NP CC:: TALL

\I 0:===

i SPACE 2 OT\/

OQUTINF.:5 FOP ZIGET =============================8=============8=6

<;Pl\CE l

.I *--------~OUTIN~

~LL'1ET ~~U GETMAIN

~*

TO GWT ALL cn~E VCeLA=~ETALL,A=~80P.SO=O AVATLABLE I l TP c:iz A 8 EN I) c:q5,;:ns (0.~lOl 111 ? 0 * !J '1 'Ac C::P.:'.Cf l I *--------POUTPIF.:

FDEFnv~n ECU 0 TO F"qF'.F.: 5YSTF'."' OVEP~EAI')

F~EEMA!~ V*A=OE5A!J'1eC::~=O I SDt.<:E 1 o--------ADJU<;T LF"N4 L cn,LF.:~14 F"~R CONTCOL INFOR~ATIJN S P.ESUiTH I

P7

• ST q7*LE~*IA 8R PlO

• ---------AfJJUST P.ETIJR~.1 RE*1 F"O~ CONTRL INFO I RF:T ALI_ ~au L

.s

~

p,c.

• l r:r,1 A o~.;::Ir.:-iT o---------CQMCUTE NIJ~gEP. l")Ii"'E~SIONS I

Qi:'

DTV 5ROA ~.32<~>

D n.n.(4)

RR RlO I *==== ~NTPY c:;PACE '2 POINT ~nR 7-IFPE~ =========================================

CALL ZIFCEE CA,o) ~H~RE, I A

= AOOPE5<; 0F" MAIN STO~AGE TO 8~

= ERQQR RETURN STATE~ENT NU~8E~

FREEO ENT~Y ZIFqF.:t:

• I qc OC i~.12co,1si X*7*

-145- I DC CL7'7fF:JEF: I STM nRnP ll..-l~d2(13l 1?

SAVE RE3ISTERS. I l.P 11 ol c:;

USTl\JG SR TM ZT~:;,C:::'1 ic;.is

!)(ll*"'q0' l

TEST Fn~ RIGHT NO. OF ARGUM~NTS I

~z L

SLL f:OCTC 2.n(Q.l>

1.1 LOAD ~OJR OF AREA TO 8E FREEn TPY AGAI~-MULTIPLY R7 BY ~

I QCT 6*L00P LA 15.4<'1,0l ERQOR R~TURN (PF.:TURl\J l>

I 8 C!FTUP~.r MVC TPANSF'Fc TO F'OPTOAt-r TRACEBACK R::>UTINE IC:::N+2t2l *2(l4l PTCK UP I~TERNAL STATEMENT NUM8ER I l~ l *PLIC:::T L

8Al.q lS,tRi;:~

14'15 II L 3.4(0.2l R3= NO ::>F BYTES TO 8~ RELEASfD STM  ?.J * .1nn~

FREE MA I 1\1 V

• A= A0 0 P

• oPnJ (~NAPr)Cg,

~ o: 0

<OUTPIJTl) FOR DE~UGGTNG PU~POSF:

• ,1

-!> SNAP DC8=9JO.OOC8.J0=2*S.JATA=(C8l ,?OATA=REGS OEBUGG PC"TIJRM E!1J CLOSE F.QU f:QU (SNAPQC~l FOR DEBUGGING PUoPOSF:

I L

l LM ll..d2(13l Rl.ADOR 2.12,2~rl3l I

'-1VI l?(lJJ.x*n:*

• "I APl)Cf3

~CP l)C8 15.}4 PETURN 0SOcG:P5,RECFM:V8A,~ACqF=<Wl *8LKS!7.E=ln3~,LRFCL=125, I

OONAME=SNAPCACn FOO DEBUGGING PUPPOSF Pt_ r c:;T I c::; l\J CIC oc A ( TSN l F 11'1' INTEqNAi_: STATE"!EMT NIJ~BED I

LF:NGTH OOGLGTH AOOR

!JC oc DC P:' n '

F*nr P:' n '

LENGT~ JF STORAGE REQUESTED.

LENGT~ OF STORAGE RE~UESTED.

ADORES~ OF 5TOPAGE ALLOCATED (MIN>

C~AXl I'

.LENA f"JC F' (l I l~NGTH JF STORAGE ALLOCATED qc:-G2 DEG3

~S:::Gf:i 115 ns ns lF lF lF AOOR. OF DUMMY VARIA8LECAPGll ADDRESS OF AREA TO BF RELEASFD STARTI~G AODR. OF DYNAMIC CO~E ALLOC I

~TGHT ECOOE Tr::'.ST DC DC DC FHP Ft-qqqt F' l'1 '

ERROR CODE TEST wo=<D I

IPEC! DC AOORESS OF FQRTRAN TPACEBACK ROUTINE ZERO 0'-IE QC DC V(

F*O'

!9EqH~l F' l '

I OF:SAOI) DC F I I) '

CF.:Sl_GTH GF.:TALL DC DC FI 0' F

• n*

I oc F' l 63'l4() ()I SYSOIJHO r.ic END F'l(')240' I

I

I -146-I I APPENDIX 7 I Physical Properties Subroutines I

I I

I I

I I

I I

I I

I I

I I

... 147- I c

l="UNC".TUIN

"'!~~IN NF.:w.

!-il_TQ 101 AUGUST 1074 I U=ALOG(Pl TF'(P.LE.26~.0>

LJ:IJ-7.0 GO TO 2 1-11_!'1=( ( ( ( ( (-0.5872~71 lG00*U*O. l l490AllDOl> *l.l*0.741S344A001) *U I

l*0.10~301Qc;>nn:?.> *::-tJ*O. lJP.g1384 1)02l *U*0.37492429002) *II I

2 2*0. l607'll5Anl')J) *::O!J*f}.5~715337003 PET URN

~LU:'=(< ( ( ( ( ( ( (-0.477ln-o4*rJ*0.846l8f')-03l*U-O.S339?60-02l*U l*0.12037371)n-l')ll*U*0.91')~307J-02l*U-0.6628012D-Oll*U

~*0.4l031089n-01l 0 U+0.?87b6~11D-OOl*U*0.222258SSDOil*U 3*0.13320422~02l*U*0.6Q7955J7D02 P.ETlJRN ein

• FUNCTION ...ivA>:>(O)

I MKIN NEW. ~UGUST U=ALOG<Pl

!F(o.u=:.4511.0l GO T'J ?

1974 I

U=lJ-7.1)

HVAP:( ( ( ( (0.371704l61J0l*J-0.9lll8126)0ll*U-0.244478l002l*IJ 1-0.2721717~no2>*LJ-0.442115896002)*U-0.46351642D02l*U I

2*0. l187r::i0~21')Qt..

2 i-R~TURN l*N AP= ( ( ( ( ( ( -0. 3i:i 740-04*1!-0. sar,~J')-0 3) 0 U+ 0. 4350 7598n-02) *U o* l 4 s 3 so 4 on - o1 > 'Jo'* J. o* 2 2 7 7 s 91 9 o- o1 > *t 1 I

2*0.AS550917~0>*U*o.1,22~31aao21ou+o.11os962SD04 RF.: TURN END I

c SU8POUTINE MF.:i<IN NE;.i.

X=0.001*""1 MAPqOP(P.H,(P*X~U,X~l AIJGUST 1974 1*

X3=X*X*X CP=n.864*l.~6*X-7.0*X*X*l0.5*X3-7.0*X*X3 CO=l.O/C?

XMU=O.noA*l18.0/~

I

!F' CH-qr).0) l *2*:::?

1 2

X~IJ:0.008*118.f)/(H+Q,::?c:;*:>(9Q.0-H))

X=X-0.25 I

XK=0.47-0.45*X-0.072/~XP(6.2S*X)

RETURN ENO FUNCTION ROL!Q(Pl I

c 1.1;:1<IN NE1..i.

U=ALOGCPl IFCP.L~.450.0J AlJGUST GO T0 2 1974 I

U=IJ-7.0 VLIO:((( ((-0.263Rl0-03*11*0.l426780-02>*U*0.212520-02)*U l

• 0. 119?2 70-0 2) *' J+ 0. 1974:?10-0 2) '->U + 0. 40 46Q60-0 2) *I.I I

2*0.219~328nn-1 ROLIO=l.O/ilLIQ

~ETURN I

2 VLI'1=! ( < ( ( ( co*.£i.6RD-08*11-0.7470-07>*tJ*O.J96960-06)oU l-0.369450-0~)*1J-IJ.204944J-03J*U*0.674627980-0S>*U 2*0.3313273~n-04> 0 U+O.lOJ94Sl40-03)ll-U*0.16l40836D-l QOLIQ=l.OIVLIQ I.

RETURN ENIJ FUNCTION QOVAPtP)

I

-148-

• ~ F'. !< I N NE 1..;

• A1Jr, i J c; T J en 4 ll=ALOG(PJ IFCP.L~.450.nJ GI") TO ?

U=l.1-7. :J DVG= C ( ( ( ( *1. 4 74~R 752110 l ';' 1-0. 639 l 3524n0 l l *U-0. ??430A05002 l *11 1- () * ?. 796 7 0 541"l 0 2) *' J-1). s 111('I72..j2[l0 2) OIJ-0. 6151469 l D 0 2) ou

~+O .439974~4ii01 Rf)VAP=P ;Pvr-.

C<F'.T!JRN CVG:( ( ( ( ( ( (-IJ.1Ri:.i')-O~*IJ-0.1200A0-03l*u+0.672230-0Jl*U 1- 0

• 3 f) 71 3 qi)- n? ) '~I J- 0

• f, 3 1 l ? 6 o- a 2 )

• u + 0

• 6 0 0 0 1 6 2 9D- 0 1 ) * ! I 2 + o. 11o3qJ1sno1 > *'* 1+11. 1c?.S7 40 loo 2 1 *IJ +a. J 336 o o 56G a 3 R()l/AP:P/Pifr; RETURN F.:NO F!JNCTIO~~ 5'1TTF:*A(OJ

~~l<IN l\Jf:\"* ~1JG:JST 1074 U=Al_OG (Pl IF(D.Lr:.i:+.sn.ni GO TO 2 U=IJ- 7. I)

SATTE~=C(((-0.16074225n-OO*J-l).A967~57600l*tl+0.6178ll1900l*U 1 +O. l46S778Jll02l *'J*O. l::?4115875D03l 0 11+Q.5SS99496fJ03 PETUP~ .

5ATTEM:((I( ( CC-O.l9~0-05*U+O.l4050-04)*U-3.2650-Sl*U l*2.3907D-3l*U ... l'l.4346l>:in-02l*U+0.1736300400l*IJ+0.2?A0814900ll*!J

?.+0.3344677i:.fi02l*U+0.101~2492(')J RFT!JP~J em SU~POUT!i"JE c:;uPTF'.\I (P,R!_ .oG,STJ MEK IN NEi.v. AU.GUST 1q7!..

x=RL -~r,

.X=0 .. 00000l'!l'l(**4 ST=V*(4.6n+l.R4/~XC(n.~~3*Xl*0.232*FX~Cl.56*(X-15.0)l}

5 T=S Tl:-f,. BS:::>t::;~-115 Rf TURN ENO

-149-I I

APPENDIX 8 I

Coding of Subroutine BAROC I I

I I

I I

I I

I I

I I

I I

I I

I -150-I ~u8qOUTINE nt

1.

• M~ N 5 !

~APOC(IPAQr,c.Q,Gwv.F~ULT*~orJ 0 ~~ A l ( 4 l ' A 2 ( 4 l

• c (1 :a a ( l 4

• 7 ) ' c C) :: ::" ( l 2

• 8 } ' n A T ( 1 2 ' 5

• s ) ' 't ( c; .>

GG ( 7 l , 'IQ ( l 4 l

• cc <8 l , ZNN ( 3. 6 l n ~ T ~ z~' ~u l

• 2 6 2 l , o

• 6 7 4. q

• n

• o 7 3

• 1

• gs 5 1 , 1

• o o4 3

• o

• 1 o q 7

• l ~ 4 g A5

• n

• A4o ~ * .

I lO.OQ71.o.7g~s.o.SSJl,O.Ob73.0.77l.0.5638.0.0713.0.483~.0.47g3,

?Q.(li:-57/

OATA CPv0.0001.o.001.n.~04,0.01.0.03.0.1.0.3,1.01 I n4TA GG/O.n.0.25*0.S*l.0*2.0,J.O,lOOO.O/

DATA Q010.o.o.on1.o.01.n.03s,o.os.o.01s,o.1.o.1s.n.2.

1n.1.o.4,0.A.o.~.1.01 OATA COEF12.2.9.2,2~.S.47.Q,99.o,16J.O,J76.0t630.o.130Q.0,20SO.O.

I l 4300.C * .'J600.0,

? 2.1s.s.a.~~.s.34.2,4~.~.10.o.1os.o,1~8.o,240.o.3~0.o,s3a.o,160.o, 1 2.os.1.s.1~.J.22.a.~q.o,J6.o,49.S,~J.o,86.o,110.o.1s~.o.?01.o.

I 4 1.~9.4.8,Q.6.12.4,16.o.20.o,21.o,33~s,4J.s,sJ~o,69.o.~s.o, s i.12.1.s1.1.~s,4.7,6.1.1.9,11.o.13.2,118J,21.2,2~.o,30.o.

~ 1.P4.1.22.1.1~.2.ns.2.~.2~a,3.6,4.2*3.s.6.s.e.o,q.1, 7 l.01.1.06.1.2~.l.36*1.5*l.S9,1.77*l*9J,2.2S*2.48,2.86.3.?tl2°1.0/

QATA OAT/l,6~9.l.669*l.~26,l,6el.59,l.58*l.S8*1.S~,l.S34, l l.492.1.362.1.178.

2 1.l~*l.158,l.059tl.O*l.21.l.42*l.42,l.42,l.324*l.234,1.l19*1*103,*

I 31.22,1.301.1.J5s.1.3g4,1.so2.1.J6.1.J6,1.J6.1.31,1.34,1.1~2.1.0~6*

4 l-.ll,l.166,l.42,1~572,1*6~5,l.818,l.81R*l*Rl8*l*~l9*1.44St s 1.204,1.01.12~1.o.

6 l.J,l,J3,l.3lltla3tle3tl*3,l.304,l.308,l.284,l.2Atl*2*l*l*

I 11.1J,1.2s.1.11.1.12,1.14s,1.216,1.2so.1.2J6,1.19s.1.1~3,1.11.1.n1,

~ 1.1.1.1s.1.1s,1.214,1.21.1.219,1.2~3*1.24,1.2Js.1.2J,1.13,1.0~4, 9 1.01e,1.oa5,1.232,1.12.1.334,1.4~o.1.412.1.s96,l.4S7, I 4 l.Jl~*l*l~4*l.0Al,l2*1.0*60*1.0,

~n.15.o.74,n.74~,n.7S4.n.1s2,o.1s.o.1J6,o.12?*0.74~.o.17,o.82.o.91, r ~.g64,0.66*0.~7~.o.6RA.0.704,o.721.o.746.o.1s,o.1ga,n.ao~.o.e6,

~ o.qJ2.o.9as.o.~~.o.s~9.o.19a.o.aos.o.a12.o.1aa.o.164.o.7~.

I ~ n.~qf,n.10~.n.R~,

~ n.97.Q.ql?*0.~17.o.76.o.73.0.7*0.6~5.0.63,0.602,o.574,0.574,Q.7, G l~*l.o.0.63*0.61,0.~~5.0.634.0.634,0.634.Q.6n~.o.S9~.o.6,4.0.65.

I ~.11~ ** ~36 ** 1s ** 4~4 ** Sn1 ** s12 ** 5~1 ** 59,.60S ** 62,.6~7,.7l4,.7~2 ** 8a, T.8A~*.81,.74l ** 7 ** 7Ql ** 702,.67J,.64J,.S9J,.542~.S42te69,.q37,.R84t

.J .,7~9 ** 1,.~71 ** 642,.587,.540,.493 ** 454,.454 ** 58.l::l~l,;n/

I OATA 5~/0.2~0ll2*-0*2Q9745,0.440706,*0e325A?3/

naTA Al/2.46896E-04,l.Q~S08E-Ol*-3.1~163~-02.2.64J63E-Ol/

~ATA X/-8.25~8J,-5.S7275~*-2.8647.-l.6lq488.0.0/

I c 7LTNCXAtYAoXC.YC*XBl=(CYA-YC)~X8+(YC~XA-YAoXCll/CXA-XCl 7.P~CT<Xl*X2*YloY2tZll*Z12*Z21,z22.xx.YY) =

l { (Y2-YY)*(Zll*<X2-XXl

• Z2l~(XX-Xlll I \,

~ - C'fl-YYl*<Zl2*CX2-X'()

• Z22-i>(XX-Xlll l 1 /((Yl-Y2l""CX1-X2l)

~L!~E I~ V!LUE OF YB AT XS,  !~TEPPOLATED LINEARLY 8ETWFEN CXA.YA)

I ~

c A"-10 ( XC

• YC l

~PCT IS VA~UE OF Z AT rXX,YY>* LINE~~LY INTERPOLATED 8ETWEEN Zll AT (Xl.Yll* ZJ2 AT cx1.y2), Z21 AT cx2.Yll ANO Z2? AT cx2.Y2)

I g. !CAPT

!CART

=

= 2.

1, ENTE~ ~IT~ P~ESSURE ANO S~T ARRAY CORAg ENTE~ WITW MASS VELOCITY AND ~UALITY. INTEqPOLATE c IN C0RA8 TO OBTAIN MULTI~LIER.

I c IF' (!CART .~Q.2l GO TO 41 SET P~YSIC~L PROPERTY TN~EX FROM PRESSURE.

c

!F'((P.LT.ll.42ql.OR.(P.r.T.3204.0ll P~I~T lOOl*P I !F'(P.GT.1429.Sl GO TO-~

-151-I YY=Al(£+J no 2 I=l*J L=4-I I

Ill

? YY=YY*~/]2n4*Al

1'.(

~0 TJ l?.

= yy I q C01<.JT I ~*!UE yv:A2(~)

rin 10 I=l*l I

L=t:..-I 10 YY=YY*C/3?n4*A?(L) 1~

OX :

oor YY*P/(]204-~+YY*O)

= AL0G(PX)

I 1, CO"'!Til\JUE i'.MA:X=l4 IF(OX.LT.PO(l))  ;:>X = PPCl>

I J=l iu. ri=-(ox.u:.Po1Jll c;o ro l~ 1~

,J=J

• l GO TO lt..

c c

t6 c:;ET MULTIOL[=:;i AT G

~n 22 I=l.TvAx

= 1.0 I IFCI.EQ.ll C1~A8(l.4l=1.0 IFCI.E~.IM4X) CO?A8([MA'.(*~l=l.O/PX I F ( ( I * ;: Q

• l l

• 0 R * ( I

• E Q

• I *~ ~ 1- l l G0 T 0 2 2 I

"4=!-1 IF"(J.GT.2J GO T'1 15 1..J V =7 L I 1'1 i: ( AL() G ( Po Cl l l , Al(') G ( C :>EI=' ( ~ , ll l ' A. l 0 G ( PP ( 2 J l , Al 0 G ( C0 E F ( M , 2 J l ,

I l PP I)

Jc:;

COPA8(!e4):1='XP(~Vl GO TO

!l="(!.G~.-'1)

~2 GO Tll 17 I

!FCCJ.LT.41 .~~. (J.GT.511 Z~=~XP(ZNN(l,Ml+ZNN(2.~J*PPT+Z~N().M1*PPI*OP!)

GO TO 19 GO TO 17 I

17 IF (J.LF.7> GO T:J 18 t./V = ZLINEIAL0G(OP(7) J eAL0GCCOEF'P."'*7l >, O.Q,Q.Q,PoIJ COPA8(T.4l:fXP(WVJ I SO TO ?2

!'3 !FCJ.~~.ll Zt\11 J=2

= .ALOGC (COi:'.F(~.J-ll - l.O

• QQ(!) l*PP(J-1> )/AL_OG<QQ(!J)

ZN2 = AL0G((COFF(M,J l - l.O

• QQ(Ill*PP(j ))/AL~GCQQCI>l I

lO f)

ZN= 7LINE(~L0G(PP(J-1l l *ALOG(ZNl> .ALvG(PP(J)) *ALnG<Z~2) ,PPJ)

Z"'-1 = F.:XP ( z,,)

r. p A 8 ( T

• 4 l = 1

• 0 - Q T ) + ( QQ ( I ) ...

• z Ip I) ( \j ) '-<.

I 22 CONT I"!tJE c

c SET en~ A3 I

'"'1.0. nn x tJS PJ<; l..1 ~ss VELOCITY coq~~CT I ON F ~CTOP. I 1'. l\ff) =

1 1

• I) 30 Fl!T=O.lc::;

TF'(PPT.LT.~t'(P,tl")l*lll I NO l =I \lO 1

• 1 G() TO 32 I t;Q TO 30 32 P-102=0. 0 DO 34 K':2.4 I

34 TI=' < CPP T

• GT * ( X ( I<'. l -'3 I T l l

• A \I 0 * ( o D I

• L T * ( X ( K> + 8 I Tl l l I "' 0 2 =K f)O "l=I-1 38 I=l-!MAX I

I -152-I I i:-

'-1= J-1

( ( I * ~ '1

• l l

• A '*Jn

• CJ

• LT

• 7 l l .; 0 T 0 3 5 IF ( ( !. ;:_: 11 .r ... ox )

• A\In. ( J. '** T. 7) ) r;n TI') J 3 I TF(..J.i:-,1.ll Tl:"(..J.F*l.7l

=

.. =J GO T1 .17 y y 7 L Ti'J i:: ( x ( r !\j I! 1_ )

• DA T ( "'

• T\j Dl ' ""'

• x ( r '.\J f) l + l )

• I) AT ( N* I \In l + 1

• M

l. l

• oi:i I l I.  ! F CP.I ~ ~

• E *1

• I'\

• 0 l G0 T n 3 ~

=

X l 'i ( P.1 0 2 ) - ):I I T

't 2=X ( PJf)2 l +;;IT

=

I Y l 7 L I l\J ~ ( X CT'Ir/ 2- *1 l

• 0 ~ T ( l\I

• I *'-J) 2- l * ~ l

• X ( I \J 0 2 l , [')AT ( N , T \J 0 2 * ~ l , X l l V?.=7LPJE(:.<(T'rn2l oDAT('J.T\J02oM) oX{I!\Jfl2+1> .OAT(NdNl'.'2+1,M) ,'t2) y Y=n , c; * (ZL T1\1 E Cx l , Y l , x? , Y 2

• P;:;) I l + YY l

'iO T() J~

I JS YY=l.O 1A CORA8C!.Jl=YY*C0~A~(T.4l t;IJ TO ~.'I I 37 COPA8rI.Jl=l.O l~ CrlN!

RF::TUP"t p..11J~

I c 41 JNTF"GPOLAT~

G=GWV*I.0~-0~

IN cn~a8 aooAY ro F"INn MJLTIPLIEP.

!F<G.GF.lonn.01G = inno.o I 42 T"-101=1 IFCQ.LE.QQCT~ntl I"IDl=INOl*l l GO T0 ~4 GO TO 4?

"I

., 44 <:ONTil\JUE 4~

!..~

T"IC2= I Jl:"(~.LT.GG<r~n

!'ID2=I"lf!2+ l r:n TO 4.6 G?=GG ( P*iJ~ l GOT~ 48 G l =GG CT'-102-1 l I Gl=G TF ( G

• I_ E

• l , r, ) GIi TI') c:; n r..1 = l

• n /i. l I ~n

. (';2=1.

G"3=1.Q/G3 1".:0NTINUE r.:i /(i2 211 = CORA~CINn1-1.r~n2-ll 112 = coR~~,r~o1-1.r~n2 >

7.21 = CORAl=lCINnl ,p.Jl');:>-ll Z22 = CORA81I~Dl .r~n? )

Xl = QQCI\IGl-ll X2 = (jl)(I"'1'1l xx =~

FMULT = zo~~TfXloX2.G1.~2*Zll,Zl2,Z2l*Z22.xx.G3>

OO!=ALOGlO(~XP(P~Il)

- PE'T\IRN c

1!')I')1 F"QPMAT (' O~ESSU~E = I. lPEls.~, 1 oJTsroE vALIO oANGE OF 11.43 ro l 1;:!')4 OSIA*)

E"t0 I

-153- I I

APPENDIX 9 I

SEPRAT Coding I

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I -154-ICr, FL()~ ITE~~T!ON FO~ S~PAPATEJ CHANNELS (EG 8WPl I~r. CALLED FRO~ sc~~~E SP usi:o F00 (l> :JM;l)P c2i J..., (3> o?

i:

I c IMPt_ICIT !t-.JTEGl=.:::J ('5) coM~o~.J 1cn=loA1.1 ARETA .AFLux ,ATOTA*-:*8BETA ,ou ,or .ox ,

I ~

1 I t:LEI/ .F'~~OnP.FLn HFG J3

.~G

,J4

,12

.JS

.~T-1

.IJ

,J6

.Ge

,J7

• GK

.IERRO~tIQP3

.GRID ,Hc;uRF tHF'

• ITERAT,Jl tKOEBUGtKF' ,KtJ

,J2 4 NAFACT.~A~hMC.NA~ .~AXL ,NR8C *NCHANLtNCHF tNDX ,NF ,

I 5

~

NGAPS .MGPin eNGPinT.~GTYoE,NGXL t~K NRA~P ,l\IPQI) .NSCC1C ,~V ,NVISCNtPI

• NOOE~ tNODESFtNPPOP

.PITC~ ,POWER ,PREF ,

7 ~AX ,~HOF' .PH0~ .SIG~A ,SL tTF tTFLU!DtTHETA tTHICK ,

le ~ 11F .vF CQMMQN /C()QoA?/

.vFr, .vG .z AA(4). AF(7), AFACT(l0,10), Al/(7), AX!AltJQ),

1 tiXL<l'1l. ;:iqc4l

• RX()r.l, CCC4l, CC~ADC2l

• CFUELt~l, OFUFLf2>,

I '.2 1

GAPXLClti), c;FACrcg.iri>. GRIDXL(l()), HGAPC2). H!-IFCJO)t HHG(JQ),

IGPIDCll'll

• K'CLAf)(2l, -<FUEL<2>, ><"¥.'"C30l

• NCHClOl, NGAPC~>,

4 r:>P(30>, PCL~D!2J,P.Fl1F:LC2>,5SIGMA(30J, TCLADC2l, UUF'C30lt S VVF(JOl, VVGC30l * ;u)1JAL(30), Y(JOl

• TTC30)

LOGICAL G~ID

~EAL Kf.J, KF. KKF, KCLAD, ~FUEL CO~MON /CQgPA]/ MA .~C ,MG ,MN ,MR ,4~ ,MX ,

l ~<;$ ,$A .SAAA .$AC *SALOJ..iA,~AN ,$AMSWF,$8 ,

l ~CCHAN,c;co .ic~Fq .ICON .§CONO .scP .so ,$OC .~OFDX '

~ <:;0!40X ,q;f")J..iYI") ,SOHY0~1.SQIST ,$DPOX ,$QPK t'bDUR ,$(')R ,SF

• I 1 4

5FACTO.~F'OIV .5FtNLE.iFLUX ,SF~ULTtSF'OLD t5FSP

~GAP .~~AP~ .~GAP~ .BH tSFSPLTt~FXFLO*

,$HFIL~*$HINLE*SHOLn ,$HPEQT,$J(')ARE, t; *;;roF1_1E,c;toG-oC,'£IK ,$Jr30ILe1iJK tSLC ,'l;LENr,T,$L(')CA ,$LR I ~

7 R

SMCHFR.~MCFoC.SMCFOP.~NTYPE,~NWRA~,$NWRPS,$P

$PHI

$0UAL

.~P~NTC.~PPNT~.~PR~TN,5PW

,~OAl)[A.~RHn .~R~OQL,$SP t$PWRF ,$QC

.~r

sr

>~R!~,5PH

,$QF ,~QPR!~*

.srou~Y,$TINLE*STROD 9

.svrsc t$V!SCWt$VP I c g

A

<fiU

~w

,1.tlJ!"'f

,,WnLn ,$WP

.~USAIJS::.iiUSTAP.SV

,$WSAVE.SX t$XCROS

,$VPA ' ) -~ .

COM~ON DATACll I LOGICAL L')ATCll PHEGER Il)t.T Cl l EQUTVO.LENCF.: COATACll ,[nATCl> *LDAT<ll l I~ !F' <IPA~T.=-~.2> SO TO 111 on 2 I= 1 'NC:i-IAl\jl_

I ~ 1 OATAC50FDX*tl=O.O OATACSF*!*~C*CJ-1>l=OATACSF+I+~C*CJ-2ll-DX/DT*CDATA($PHO+!*MC*(J-1SEPRAT ll-OATAl~RHOOL+!+~C*(J-llll~OATA($A+Il

. ~EPRAT Ic CALL DIFFE:::>cJ,Jl RF.:TIJRN ll'l PMIN=looooo.o I PMAX=-1000.0

-155- I

=

r) 0 l 2 I l * "IC' i-1 Al<J '-

'11 V=OAT A(<l5P*T)

IF (WV.LT.OM!~) ::JMIN=WV I

IF (*.1'V.GT.OMAX) ::JMA'(:WV 12 CONTINUE" T~Crl.o-~~TN/P~A~l.LT.FF~RQ~) RETURN I Jll'-1P= l IFCifERAT.GT.ll 30 Tn l"-

FT0T=O.O DO 14 I=l*"ICHMJL I

FTOT=FTGT+~ATA(~F+\)

f)ATACf:SO+IJ = '1.l*DATACc;;SP+Il I F (Q ~ T A ( c; 5 P + I I * 'IE

• 0

• Ii l 3 0 i 0 1 4 I

OATAC~5P*T)=0.7*0ATAC3F*I)/(0ATA($P+Il-0AiAC$RHO+I+MC*NDXl*

l ELEv~~z}

SEPRATI 14 CONTINU~

GO TO 20 l~ QO 18 I=l.~C~ANL lR OATA(iSP*Il=COATA(~F+T)-JATAC!5P+I+~Cll/C0ATAC$P+Tl-DATAC~SP+J+ sE=RATI 1 2*M() )

20 Si.J~l=Q.O 5!.J"'llJ=O.O

=

!J 0 2 2 I l

• 11..1 <: !-! A ~ l L I

5UYl=SUMl*nATAf~SP*Il SUM13=SU~l3*0ATACi~P+TJ*JATA($P+Il OATA(~SP*I*~Cl=OATA(~F+Tl I 22 DATACSSP+I+MC*?l=DATAC~P*Il SEPRATI SUMF=n.o 00 24 I::l,"-!O*~Al\IL OATAC$F+Il=OATAC~F*Il+OATAC~SP+Il*CSJ~l3/SUM1-0ATACSP*Ill

?4 SUMF=SUMF*~ATA(~F+Il

?~

00 26 I= 1 * !'!Ci-IANL OATAC~F+IJ=OATAr~F+Il*FTJT/SU~F SEPRAT I

PTURN ENO I

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I -156-I I APPENDIX 10 I Input Data Preservation Based on that of COBRA IIIC I

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-157- I card(s) Type Cl Problem Array Size I Required *to be present.* Always FORTRAN READ list:

• MC MG MN MR MX I FORTRAN FORMAT: 10!5 Read. from Subroutine: INDAT I

I Variable Columns Format Description CG MC 1-S IS ~

> No. of channels (NCHANL) in pro- I

• blem. NCHANL is set from NTHBOX on cards CS-C7, or in the original COBRA format, in Card Group 4. I

~ No. of gap interconnections (NK)

MG 6-10 IS between channels in problem. If this is not known, MG=Z*MC is usu-I ally adequate but should be checked later. For a BWR, MG may be given as zero, when it is reset to 1 in I

CORE.

MN 11-lS -IS ~ No. of fuel nodal points in problem.

This should be ~ (~ODESF+l) on Card J

Tl. If MN is given as zero, it is reset to 1 in CORE. I MR 16-20 IS ~ No. of rods (NRCD) in problem.

For PWR and BWR, NROD=NCHANL, hence MR may be given=MC.

I MX 21-2S I.S ~ No. of axial stations in problem.

It may be given as NDX (Card Cll) as it is increased by 1 immediately I

after reading in.

Notes I

(1) MC to MX are used to set the array sizes in the dynamic sto-r,ge, hence they should be set too big r*ther than too small. I (2) Note that MC to MX are given in alphabetical order.

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I -158-I.

~* '

Card(s) Type C2 Required *to b*e present Maximum Running Time Always I FORTRk.'1 READ list: MAXT FORTRAN FORMAT: IS, 6E12.6 I Read. from Subroutine: INDAT I Variable Columns Format Description CG I MAXT 1-5 IS Maximum Running Time, Nominal value is 2000.

c o*

N I T R

0 I L I

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I 1-1 I

I

-I

_)

I

THE INPUT FOR A CASE REQUIRES A CASE CONTROL CARD FOLLOWED wrrrH UP TO 12 GROUPS OF INPUT INFORMATION. EACH OF THE 12 CARD GROUPS HAS A GROUP CONTROL CARD THAT IDEWrIFIES THE GROUP NUMBER AND THE OPTIONS J\VJ\ILJ\BLE FOR THAT GROUP.

I O'\

l.f\

r-1 1 GO TO THE CARD GROUP SPECIFIED BY NGROUP, IF THE DATA OF A CARD GROUP THE SAME AS THE PREVIOUS CASE, THEN THAT CARD GROUP AND ITS CONTROL MAY BE OMITTED.

I -160-I Card C3 I Cards (s) Type C3 Case Control Card Required to be present Always I FORTRAH READ list IPILE, KASE, Jl, TEXT I FORTRAN FORMAT Read from subroutines Il, I4, IS, 17A4 I HD AT I

I Variables Format Columns Description I PILE Il 1 = 0 I KASE I4 2 - 5 Run identification number.

If > o, calculation continues If~ O, calculation stops.

I Jl I5 6 - 10 Printing option for standard I COBRA output - as in COBRA III-C.

= 1 print entire output I =2 print only operation conditions I

TEXT I7A4 i l - 78 Alphanumeric information to identify case I

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-161- I I

Card Group 1 Always Required to be present HGROUP lH I

FORTRAll READ list I5, I5 IHDAT I

FORTRAN FORMAT Read from subroutine I I

Variable Columns Format Description I

I NG ROUP 1-5 I-5 =1 (to select Card Group 1)

I I

6-10 I-5 < 0 calculate physical properties from polynomials I

> 1 the physical properties' are given in the next J Cards as in the original COBRA.

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I -162-I Physical Properties I

Required to be present I

i FORTRAN READ list when Nl(in Card Group 1) < 0 H PH P2 iH I FORTRAN FORMAT READ from subroutine I5 Fl0.3 FlO. 3 I5 CARDS l Variable Format Columns Descrintion I H I5 1-5 = 1: PH defined as lm*iest pressure encountered in problem.

I = 2: PH defined as lowest enthalpy encountered in prob len I PH Fl0.3 s-15 Lowest pressure (psia) if Nl = 1 or lowest enthalpy I (Btu/lb) if rn = 2.

I P2 Fl0.3 16-25 Highest pressure (psia) encou.'1tered in problem.

I Hl I5 26-30 Number of pressure steps generated by polynomial (maxi.mum 30)

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I lfotes:

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-163-I I

The lowest pressure encountered in the problem is defined as that at which the lowest enthalpy would be the saturation I value. For example, at 1000 psia the saturation enthalpy is 543 Btu/lb *. At an inlet subcooling of 100 Btu/lb, the enthalpy I

would be 443 Btu/lb and this would be the saturation value at I a pressure of about 470 psia. Thus, one would require physical property data over the range 470 (or less) psia to 1000 psia I in order to include data which covered the enthalpy ra...'1.ge.

To avoid translating the lowest enthalpy to pressure, the I

option of giving the enthalpy is included. The program trans- I lates this value to a pressure which is safely below that required using the expression I p = 6h 3 (h-1.35) I (h - 0.35) I when p =calculated pressure (psia), h = O.OlH, H =enthalpy I (Btu/lb).

The values of p, so calculated, are given below and it may I

be seen that they are all less than Psat, the tabled value of I pressure corresponding to H.

I H(Btu/lb) 181.2 300 400 500 600 700 I

p (psi a) 11 101 279 589 1067 1749 Psat (psi a) 15 103 319 745 1409 2236 I

I I

I -164-I I In the original COBRA, the physical properties are read I from cards into the arrays (PP(L), TT(L), etc., L = 1, ~,Tl).

In the new version, the values of (PP(L), TT(L), etc., L = 1, I Nl) are generated within a Do Loop from 1 to Nl from the physical property polynomials. With the arrays set, the I subsequent use of the values is the same in both versions of I the code. Note:

of the arrays.

NPROP is set to Nl for storage of the size I

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-165- I Physical Properties I

Required to be present:  :*Then :n (in Card Group 1) * > O I Read from Subroutine CARDS 1 I I

READ IH Nl CARDS OF FLUID PROPERTY DATA.

EACH CARD CONTAD-13 -- SATURATIO:l PRESSURE (PSIA), TEHPERATURE(DEG-F)

I LIQUID SPECIFIC VOLUME (CU-FT/LB), VAPOR SPECIFIC VOLUT.fil (CU-FT/LB)

I LIQUID EHTHALPY(BTU/LB), VAPOR E1J':L'HALPY(BTU/LB), LI:':lUID VISCOSITY (LB/FT-HR), LIQUID THERI:IAL CONDUCTIVITY(BTU/HR-FT-F) AHD SURFACE I TEHSION(LB/FT), FORMAT(E5.2,F5.l,7Fl0.0). iH MUST BE GREATER ':1HA.N ONE BUT NOT GREATER THA1l THE PARArETER MP.

THIS PROPERTY TABLE I1UST HAVE PRESSURE HIGHER THAN OPERATING I

PRESS. AND LIQUID ENTHALPY LOWER THAN THE BUIJDLE IULET ENTllALPY.

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CARD GROUP 2, FLOW CORRELA'1 IONS 1

READ IN UP TO FOUR SETS OF FRICTION FACTOR COHRELJ\.TION CONSTANTS THAT CORRESPOND TO THE SUBCHANNEL TYPES, FORMAT(l2F5.3).

Nl IS THE SUBCOOLED VOID CORRELATION OPTION. Nl=O, NO SUBCOOLED VOIDS. Nl=l, LEVY SUBCOOLED VOID CORRELATION.

N2 IS THE BULK VOID CORRELATION OPTION. N2=0, HOMOGENEOUS MODEL.

N2 = 1, MODIFIED ARMAND MODEL. N2 =5, READ IN SLIP RATIO, FORMAT (5X,El0.5). N2=6, READ IN THE NUMBER OF TERMS AND COEFFICIENTS FOR UP TO A SIXTH ORDER POLYNOMIAL FUNCTION OF STEAM QUALITY, FORMAT I

(I5,7El0.5). I-'

CJ\

CJ\

I N3 IS THE TWO-PHASE FRICTION GRADIENT MULTIPLIIm OPTION. N3=0, HOMOGENEOUS. N3=1, ARMAND. N3=5, READ IN NUMBER OF TERMS AND COEFii'ICIENTS J1 0R UP TO A SIXTH ORDER POLYNOMIAL fo'UNCTION Qli' QUALITY 1

FORMAT(I5,7El0.5).

Nit IS AN OPTION TO INCLUDE A WALL VISCOSITY CORRECTION TO THE FRICTION FACTOR. IF Nll=l, IT IS INCLUDED, OTHERWISE I'l IS NOT.

1 CARD GROUP 3, AXIAL HEAT FLUX TABLE READ IN Nl PAIR OF DATA FOR THE TABLE. EACH PAIR CONSISTS OF TIIE RELATIVE POSITION (X/L) AND THE CORRESPONDING RELATIVE HEAT FLUX (LOCAL FLUX/AVERAGE FLUX). EACII CARD ACCEPTS UP TO SIX PAIR OF DATA! FORMAT(l2F5.3). Nl MUST BE GREATER THAN ONE BUT NOT GREATER THAN THE PARAMETER MP.

CARD GROUP 11, SUBCHANNEL LAYOUT AND DIMENSIONS READ IN Nl CARDS OF SUBCHANNEL DATA CORRESPONDING TO THOSE SUBCHANNEL FOR WHICH DATA ARE BEING SUPPLIED. N2 IS THE TOTAL NUMBER OF SUB-CHANNELS. FOR EACH OF THE Nl CARDS, READ IN THE SUBCHANNEL TYPE NUMBER (IF BLANK, IT IS ASSUMMED TYPE 1), SUBCHANNEL IDENTIFICATION NUMBER, NOMINAL FLOW AREA(SQ-IN.), WETTED PERIMETER (IN.), HEATED PERIMETER(IN.) AND UP TO FOUR SETS OF ADJACENT SUBCHANNEL CONNECTING Ilfli'ORMJ\TION, I~ORMAT(Il,I4,3E5.2,1HI5,2E5.2)). EACH SET OF CONNECTING INFORMATION INCLUDES THE ADJACENT SUBCHANNEL NUMBER (NEGATIVE IF A LINE OF SYMMETHY SPLITS A GAP AT A BOUNDARY), NOMINAL GAP SPACING I

AND CENTROID-TO-CENTROID DISTANCE(IN.). IF SUBCHANNELS ARE INPUT IN I-'

0\

--1 ASCENDING ORDER, THEN ONLY HIGHER NUMBER SUBCHANNELS NEED TO BE I IDENTili'IED AS CONNECTIONS. CENTROID DISTANCES ARE NOT REQUIRED IF THEY ARE NOT USED IN THE MIXING COHRELATIONS. N2 MUST BE GREATER THAN mm BUT NOT GREATER THAN THE PARAMETER MC.

--~----------------

CARD GROUP 5, SUBCHANNEL AREA VARIATION TABLE IF THERE ARE NO AREA VARIATIONS, OMIT THIS CARD GROUP.

• READ N2 VALUES OF RELATIVE LOCATION(X/L) WHERE AREA FACTORS ARE GIVEN FORMAT(l2F5.3)~ N2 MUST BE GREATER THAN ONE BUT NOT GREATER THAN THE PARAMETER ML.

READ Nl SETS OF AREA VARIATION FACTORS (LOCAL AREA/NOMINAL AREA).

EACH SET CONSISTS OF SUBCHANNEL NUMBER AND N2 AREA VARIATION FACTORS, FORMAT(I5/(12F5.3)). Nl IS LIMITED BY THE PARAMETER MA.

IF Nl IS ZERO, AREA VARIATIONS ARE DELETED FOR SUCCEEDING CASES.

I N3 IS THE NUMBER OF ITERATIONS FOR INSERTING AREA VARATIONS. I-'

()'\

IF N3 IS ZERO OR BLANK, N3 IS SET EQUAL TO 1. co I

CARD GROUP 6, GAP SPACING VARIATION TABLE IF THERE ARE NO GAP VARIATIONS, OMIT IJ.'HIS CARE GROUP.

READ N2 VALUES OF THE RELATIVE LOCATION(X/L) WHERE GAP FACTORS ARE GIVEN, FORMAT(l2F5.3). N2 MUST BE GREATER THAN ONE DUT NOT GREATER THAN THE PARAMETER ML.

READ Nl SETS OF GAP SPACING FACTORS(LOCAL GAP/NOMINAL GAP).

EACH SET CONSISTS OF THE ADJACENT SUBCIIANNEL NUMBERS Ji'OR THE GAP N2 GAP VAHIATION FACTORS, FORMAT(2I5/(12F5.3)). IU IS LIMITED BY PARAMETER MS. Il" Nl IS ZERO, GAP VARIATIONS ARE DELETED FOR SUCCEEDING CASES.

CARD GROUP 7, SPACER DATA Ili' Nl=l, WIRE WRAP FORCED DIVERSION CROSSFLOW MIXING IS INCLUDED, OTHERWISE, IT IS OMITTED.

READ ONE CARD CONTAINING THE WIRE WRAP PITCH (IN.), PIN DIAMETER AND tHRE DIAMETER (IN.), FORMAT ( 8El0. 5).

IF Nl=l, N5 IS AN OPTION TO SAVE OR USE A PREVIOUSLY COMPUTED CROSSFLOW SOLUTION. THE FLOW CONDITION MUST NOT CHANGE FOR THESE CASES NOR THE BASIC PROBLEM SETUP. THIS OPTION WOULD NORMALLY BE USED FOR CASES INVOLVING CHANGES IN POHER OR MIXING FOR NONBOILING PROBLEMS.

N5=0, CROSSFLOW SOLUTION IS COMPUTED FOR EACH CASE.

N5=1, USE FIRST CASE SOLUTION FOR ALL SUCCEEDING CASES.

N5=2, WRITE SOLUTION TO TAPE AND USE FOR SUCCEEDING CASES.

N5=3, READ SOLUTION FROM TAPE AND USE FOR SUCCEEDING CASES.

FOR EACH GAP, READ A CARD CONTAINING THE GAP NUMBER, THE EFFECTIVE FRACTION OF A PITCH FOR FORCING CROSSFLOW AND UP TO SIX RELATIVE PI'rcn LENGTHS IDENTili'YING THE LOCATION OF WRAPS CROSSING THROUGH 1\ GAP USING A POSITIVE VALUE FOR WRAPS CROSSIHG FHOM I TO J AND A NEGATIVE VALUE FOR CROSSINGS FROM J TO I WHERE I IS LESS THAN J.

THE GAP NUMUERS ARE ASSIGNED IN THE ORDER THAT SUBCHANNEL PAIRS ARE IDENTIFIED IN CARD GROUP 11.

READ IN THE NUMBER OF WRAPS CONTAINED IN EACH SUBCIIANNEL AT THE START OF rr1m BUNDLE IN ASCENDING SUBCIIANNEL ORDERJ FORMNr( 10I5).

USE ENOUGH CARDS TO SPECIFY ENTIRE WRAP INVENTORY.

IF Nl=2, SPACER PRESSURE LOSSES AND FORCED FLOH DIVERSION ARE INCLUDED OTHERWISE) THEY ARE OMITTED.

N2 IS THE TOTAL NUMBER OF SPACER LOCATIONS.

N3 IS TIIE NUMBER OF SPACER TYPES.

Nlt IS THE NUMBER OF ITERATIONS TO INSER'l' LOSS COEFFICIEHTS OR THE WIREt*lRAP MIXING. IF N4 IS BLANK OR ZERO, ONE IS USED.

I READ N2 RELATIVE LOCATIONS(X/L) WHERE SPACERS ARE LOCATED AND THE I-'

-....:i TYPE OF SPACER AT THAT LOCATION) FORMAT(6(F5.2,I5)). 0 I

READ N3 SETS OF DATA CORRESPONDING TO EACH SPACER TYPE. EACH SET CONSISTS OF A CARD FOR EVERY SUBCIIJ\NNEL. ON EACH CARD IS THE SUBCH NUMBER, SPACER LOSS COEFFICIENT, CONNECTION NUMBER OF GAP THROUGH WHICH FLOW IS FORCED, AND FRACTION OF FLOW DIVERTED, FORMAT(2(I5,E5.0))

IF 'l'lIE CONNECTION NUMBER IS ZERO AND, TIIE FLOW rmACTION IS ZERO, THEN rl'lIERE IS NO FORCED FLO\'! DIVERSION. THE FORCED CROSSFLOH HAS THE SAME SIGN AS ~IE FORCED FLOW FRACTION.

CARD GROUP 8, ROD LAYOUT, DIMENSIONS AND POWER FACTORS READ IN Nl CARDS OF ROD LAYOUT DATA CORRESPONDING TO THOSE RODS FOR WHICH DATA ARE BEING SMPPLIED. N2 IS THE TOTAL NUf1DER OF RODS.

FOR EACH OF THE Nl CARDS, READ THE ROD TYPE, NUMBER, DIA.(IN.),

RELATIVE ROD POWER(ROD POWER/AVERAGE HOD POllER) AND UP TO SIX SETS DATA FOR ROD-TO-SUBCHANNEL cmINECTIONS, Ji'ORMAT(Il,Ilt,IE5.2,6(I5,E5.0))

NUMBER AND FHACTION OF THE ROD POWER TO THAT SUBCHANNEL.

THE NUMBER OF FUEL ROD ri~YPES ARE PRESENTLY LIMlTED TO 2.

H=l INDICATES ROD FUEL. N=2 INDICATES PLATE FUEL. IN EACH CASE FOR PLATE FUEL THE non DIAr.filTER( ABOVE) IS THE PLATE THICKNESS AND I I--'

THE FRACTION OF POWER TO A CHANNEL IS THE FRACTION OF THE -.:i I--'

CIRCUMFERENCE REQUIRED TO SPECIFY THE PLATE WIDTH FACDIG THE I SUI1CllANNEL.

N2 IS LIMITED BY THE PARAMETER MR.

N3 IS rr1m NUMBER OF RADIAL FUEL NODES INCLUDING THE CLADDING.

N4 IS THE TOTAL NUMBER OF FUEL TYPES. FOR EACH FUEL TYPE, READ IN ON ONE CARD 1 THE THF.RMAL CONDUCTIVITY (B/HR-FT-F) '*

SPECIFIC HEAT (B/LB-F), DENSITY(LB(FT3), AND PELLET DIAMETER(IN.)

FOR THE FUEL 1 AND THE SAME FOR THE CLADDING EXCEPrr FOR THICKNESS (I AND r_r1rn GAP COEFFICIENT(B/HR-FT]-F). THESE ARE ASSUMED CONSTANT.

N5 IS AN OPTION TO SELECT A CRITICAL HE./\T FLUX CORRELATION.

IF N5=0, NO CIIF CALCULATIONS ARE PERFORMED. IF N5=1, THE BJ\W-2 CORRELATION IS USED. IF N5=2 1 THE W-3 CORRELATION IS USED AND THE USEH SHOULD VALIDATE THE TDC VALUE IN SUBROU'rINE CHF.

- - ~l!E~nrlflTI~PT~ c!llBE~IL"'8o\i!IW;D W.1sr-MI - - - - - -

CARD GRQUP 9, CALCULATION VARIABLES nEAD IN DIVERSION CROSSFLOW RESISTANCE FACTOn, TURBULENT MOMENTUM FACTOR, BUNDLE LENGTH(IN.), POSITION FROM VERTICAL(DEGREES), NUMBER OF AXIAL NODES, NUMBEH OF TIME STEPS, rrOTAL TRANSIENT TIME(SECONDS)

MAXIMUM NUMBER OF ITERATIONS, ALLOWABLE FRACTION ERROR IN FLOW FORMAT CONVERGENCE AND TRANSVERSE MOMENTUM PARAMETER(S/L),

FOHMAT(4E5.2,2I5,E5.2,I5,lJE5.2). IF THE NUMBER OF ITERA'.rIONS, ALLOWABLE ERROR AND MOMENTUM PARAMETER ARE BLANK on ZERO, THE PROGRAM USES 20., l.E-3, AND .5, RESPECTIVELY.

Nl IS AN OPTION GIVING THE SPATIAL P'RINTINn INCREf.1ENT. IF Nl=l, I

srrEP IS PRINTED. IF N2=-2, EVEnY OTHER STEP IS PHINTED, ETC. IF 1--'

-..:i f\)

ZERO OR BLANK, rrHE PH.OGRAM SETS tll= 1. I N2 IS AN OPTION GIVING 'J.1IIE TIME PHINTING INCREMENT AND IS SET UP SAME AS Ul ABOVE.

N3 IS A DEBUG PRINT OPTION. IF N3=0, NO DEBUG IlHi'ORMATION IS PRINT IF N3=1 A DEBUG PRINT IS MADE FOR EArnI STEP OF Tiffi CALCULATION. IT CAN GENEHA'11E A LOT OF PAPER SO IT IS NOT NORMALLY USED.

CARD GROUP 10, TURDULENT MIXING CORRELJ\:TIONS Nl IS THE OPTION FOR SUBCOOLED MIXING .CORRELATIONS. FOR ANY SELECTED VALUE OF Nl READ IN THE CONSTANTS A AND B, FORMAT(2F5.3).

rr1m OPTIONS ARE --

Nl=O, W/GS=A Nl=l, W/GS=A*RE**B Nl=2, W/GD=A*RE**B Nl=3, W/GS=D/ZIJ*A*RE**I3 UOTE THAT BETA = W/GS WHERE W IS THE TURBULEUT CROSSFLOW.

N2 IS THE OPTION FOR TUO-PIIASE MIXING. IF N2=1, Tt*IO-PIIASE MIXING I I-'

IS THE SAME AS FOR SUBCOOLED CONDITIONS. IF N2 IS GREATER THAN ONE ~

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READ IN N2 PAIR OF DATA FOR A TABLE OF TWO-PHASE MIXING DATA.

EACH PAIH CONSISTS 01" THE STEAM QUALITY AND THE CORRESPONDING VALUE OF BETA. N2 IS LIMITED I3Y THE PARAMETER MP.

N3 IS THE OPTION FOR THERMAL CONDUCTION MIXING. IF U3=0, NO THEHMA CONDUCTION. IF N3=1, READ IN THE THERMAL CONDUCTION GEOMETRY FACTOR FORMAT (F5. 3).

CARD GROUP 11, OPERATING CONDITIONS READ IN THE OPERATING PRESSURE(PSIA), INLET ENTHALPY(BTU/LB) on IHLET TEMPERATURE(DEG-F) J MASS VELOCITY(M-LD/HR-S.Q-FT) AUD AVERAGE HEAT FLUX(M-BTU/HR-SQ-FT). (6Fl0.0)

Nl IS THE INLET ENTHALPY OPTION. IF Nl=O, INLET ENTHALPY IS GIVEN. IF Nl=l, INLET TEMPERATURE IS GIVEN. IF Nl=2, READ IN THE INDIVIDUAL SUilCHJ\.NNEL INLET ENTHALPIES, FORMArr( 12E5. 0). Ili' Nl= 3, HEAD IN THE INDIVIDUAL SUBCHANNEL INLET TEMPER/\.TURES, Ji'OHMAT(l2E5.

N2 IS THE INLET FLOW DISTHIBUTIOlJ OPTION. IF N2=0, THE SUBCHANNELS I

ARE GIVEN rrHE SAME MASS VELOCITY. IF U2=1, THE INLET FLOW IS DIVID I-'

--1 TO GIVE EQUAL PRESSURE GRADIEWr IN THE SUBCIIANNELS. IF N2=2, READ .i:=-

1 MASS VELOCITY FACTORS FOR EACH SUTICIIANNEL, FORMAT(l2E5.0).

N3' Nlj, N5 and N6 ARE OPTIONS J.i'QR TRANSIEWr FORCING FUNCTIONS. IF ANY OI*' THESE OP'rION NUMBERS ARE ZERO OR BLANK, THE CORRESPOli!DING FORCING DATA IS NOT READ AND IS EXCLUDED FROM THE CALCULATIONS. EACH OF THESE NUMBERS GIVE THE NUMBER OF PAIRS OF rrAJ3ULAR DNfA TO BE RE FOR EACH FUNCTION. ALL DATA ARE READ AS PAIR~ OF TIME(SECONDS)

AND RELATIVE VALUE, FORMAT ( 12E5. 0)

• N3 IS THE OPTION FOR REFF.HENCE PRESSURE VERSUS TIME.

Nlj IS THE OPTIOU FOR INLET ENTHALPY OR TEMPEHN.rURE AS A Jl'lJNCTION OP TIME DEPENDING ON THE OPTION FOR INLET ENTHALPY OR TEMPERATURE.

N5 IS TIIE OPTION FOR INLET FLOW VERSUS TIME.

H6 IS rrim OPTION FOR HEAT FLUX VERSUS TIME.

CARD GROUP 12, OUTPUT DISPLAY OPTIONS Nl IS AN OPTION FOR PRINTING ANSWERS.

Nl=O, PRINT SUBCHANNEL DATA ONLY.

Nl=l, PRIN'l' SUBCHANNEL DATA AND CROSSFLOWS.

Nl=2, PRINT SUBCHJ\NNEL DATA AND FUEL TEMPERATURES.

Nl=3, PRINT SUBCHANNEL DATA, CROSSFLOWS AND FUEL TEMPERATURES.

N2 IS AN OPTION FOR SUBCHANNEL DATA PRINTOUT. IF N2=0, ALL SUBCHANNEL DATA ARE PRINTED. IF IT IS CALLED FOR BY Nl. FOR N2 GREATER THAN Z HEAD IN THE SUBCHANNEL NUMBERS FOR HHICH RESULTS ARE TO BE PRINTED FORMAT( 36I2). I I-'

--.1

\Jl N3 IS AN OPTION FOR FUEL TEMPERATURE PRINTOUT. IF N3=0, DATA FOR I ALL RODS ARE PRIN'rED IF CALLED FOR BY Nl. FOR N3 GREATER THAN ZERO, READ IN N3 ROD NUMBERS FOR 1HICII TEMPERATURES ARE TO BE PRINTED, FORMA'r(36I2). IF CHF DATA IS CALLED FOR BY INPUT OPTION IT IS PRINTED FOR EACH SELECTED ROD PLUS A

SUMMARY

TO IDENTIFY THE ROD AND CHANNEL WITH THE MINIMUM CIIF RATIO.

Nll IS AN OPTION FOR FUEL NODE PRINTOUT. IF N'l=O, TEMPERATURES ARE PRINTED li'OR EVERY NODE. FOR N lJ GREATER THAN ZERO, READ IN N11 NODE NUMBERS '1 0 BE PRINTED, FORMAT ( 36I2).

1 TO ST AR'r A CALCULATION, READ A BLANK GROUP CONTROL CARD.

TO STOP 'rHE CALCULATIONS, AFTER FINISHING A CASE, READ A I3LANK CASE

• * *

• END OF INPUT INSTRUCTIONS * * *

• UNI'l S - J\LL COMPUTATIONS ARE DONE USING FT, LB, SEC, BTU AND DEG-F.

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- . .IT-1\.N~FO~PU-ND-PU~ - E ~IIE~GJWll - , - - - - - -

I -176-I I APPENDIX 11 I Simplified COBRA IIIC Input Data Presentation to be used for Assembly to Assembly Analysis of LWR I

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-177- I Card(s) Type Cl Problem Array Size I Required to be present*

FORTR!>.....'1 READ list:

Always MC MG MN MR MX I

FORTRAN FORMAT: 10!5 I Read. from Subroutine: INDAT I

Format' Variable Columns

~ N Description CG I

MC 1-5 IS ,. *. 0. . of channels (NCHANL) in pro-I MG 6-10 IS

• blem. NCHANL is set from NTHBOX on cards CS-C7, or in the original COBRA format, in Card Group 4.

~ No. of gap interconnections (NK) between channels i~ problem. If this is not known> MG=2*MC is usu-ally adequate but should be checked later. For a BWR~ MG may be given I

as zero, when it is reset to 1 in CORE.

I MN 11-15 -IS ~ No. of fuel nodal points in problem.

This should b~ ~ (~ODESF*l) on Card Tl. If MN i:; gi Yen as zero, it is reset to 1 in CORE.

I MR 16-20 IS ~ No. of rods (NROD) in problem.

For PWR and BWR, NROD=NCHANL, hence I

MR may be given=MC.

21-25 IS ~ No. of axial stations in problem. I It may be given as NDX (Card Cll) as it is increased by l immediately after reading in. I Notes (1) MC to MX are used to set the array sizes in the dynamic sto-

• 1 r*ge, hence they should be set too big rather than too small.

(2) Noie that MC to MX are given in alphabetical order. I I

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I -178-Card ( s) Ty;h3 .,.. .

I.- , C2 Maxim.urr. Running ~ ime Reqtlired *to be present Always I FORTRAi.~ READ list: MAXT

• FORTRAN FORl~.Z\.T: IS, 6E12.6 I Read f=om Subroutine: INDAT I VariablG Columns Format Description CG I MAXT 1-5 IS is 2000.

Maximum Running Time, Nominal value C O*

N I T R

0 I L*

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THE INPUT li'OH A CASE REQUIRES A CASE CONTROL CARD FOLLOWED WITH UP TO 12 GROUPS OF INPUT INFOHMNrION. EACH OF THE 12 CAHD GROUPS HAS GROUP CONTROL CARD THAT IDENTIFIES THE GROUP NUMilER AND THE OPTIONS AVAILABJ:,I~ li'O THAT GROUP.

GO 'rO THE CARD GROUP SPECili'IED BY NGROUP. IF THE DATJ\ OF J\ CARD GHOU I

THE SAME AS TIIE PREVIOUS CASE 1 THEN THAT CARD GROUP AND ITS CONTROL I-'

~

MAY BE OMI'l TED.

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I -180-I I Card(s) Type C3 Case Control Card Always Required to be present I FORTRAN READ list lPILE, KASE, Jl TEXT FORTRAN FORMAT: Il, I4, I5, 17A4 I Read from subroutine IND AT I

Variable Column Format Descriotion:

I lPILE 1 Il = 1: for PWR, with interconnected channels.

I = 2: for BWR, with separated channels.

I KASE I Jl as in Appendix 10 I TEXT I

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-181-I

• I Card Group 1 I Required to be present Always I

FORTRAN READ list NG ROUP Nl I FORTRAN FORMAT IS, I5 Read from Subroutine IND AT I I

Variable Columns Format Description I NGROUP 1-S IS = 1 (to select Card Group 1) I Nl 6-10 IS < O: Calculate physical properties

• I from polynomials.

> 1: the physic~l properties are I given in the next ~n Cards as in the original COBRA.

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I -182-11I l

II Physical Properties 1\ Required to be present FORTRAH READ List When Nl(in Card Group N PH P2 i*H l)~ 0 I FORTRAN FORHAT I5 FlO. 3 FlO. 3 I5 from subroutine Cards l I READ I Variable Columns Format  :>escriotion 1-5 IS = 1: PH defined as lowest pressure I encountered in problem,

= 2: PH defined as lowest enthalpy encountered in problen I PH 6-15 Fl0.3 Lowest pressure (psia if Nl = 1 or lowest enthalpy (Btu/lb)

I if Nl = 2 P2 16-25 FlO. 3 Highest pressure (psia)

I i~l 26-30 IS encountered in problem Number of pressure steps generated by polynomial I (maximum 30).

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-183- I I

The lowest pressure encountered in the problem is defined I as that at which the lowest enthalpy would be the saturation value. For example, at 1000 psia the saturation enthalpy is I

543 Btu/lb. At an inlet subcooling of 100 Btu/lb, the enthalpy I would be 443 Btu/lb and this would be the saturation value at a pressure of about 470 psi a. Thus, one would require physical I property data over the range 470 (or less) psia to 1000 psia in order to include data which covered the enthalpy range.

I To avoid translating the lowest enthalpy to pressure, the I option of giving the enthalpy is included. The program trans-lates this value to a pressure which is safely below that I required using the expression p = 6h3(h - 1.35) I (h - 0.35)

I when p =calculated pressure (psia), h = O.OlH, H = enthalphy I (Btu/lb).

The values of p, so calculated, are given below and it may I

be seen that they are all less than Psat, the tab led value of pressure corresponding to H.

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H(Btu/lb) 181.2 300 400 500 600 700 I

p (psi a) 11 101 279 589 1067 1749 p sat (psia) 15 103 319 745 1409 2236 I I

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I -184-I I

In the original COBRA, the physical properties are read I from cards into the arrays (PP(L), TT(L), etc., L = 1, ~n).

In the new version, the values of (PP(L), TT(L), etc., L = 1, I Nl) a~e generated within a Do Loop from 1 to Nl from the physical I property polynomials. Hi th the arrays set, the subsequent use of the values is the same in both versions of the code. Note:

I* NPROP is set to Nl for storage of the size of the arrays.

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*--------*-----------**-*-*--*- ----~ **--~--****-*~--**-*--- *-*------**--*"~-----------------------*--*----

Physical Properties Required to be present When Nl (in the card group 1) > 0 READ IN Nl CARDS OF FLUID PROPERTY DATA.

EACH CARD COWfAINS -- SATURATION PRESSURE (PSIA), rrEMPERATURE(DEG-F LIQUID SPECIFIC VOLUME(CU-FT/LB), VAPOR SPECIFIC VOLUME(CU-FT/LB),

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LIQUID ENTHALPY(BTU/LB), VAPOR ENTHALPY(BTU/LB), LIQUID VISCOSITY (XI Vl (LB/FT-HR), LIQUID THEHMAL CONDUCTIVITY(BTU/HR-Ii'T-Ji') MID SURFACE I TENSION(LB/li'T), FORMJ\T(E5.2,F5.l,7Fl0.0). Nl MUST BE GREATER THAN mm BUT NOT GREATER THAN THE p ARAMErrER rw *.

THIS PROPERTY TABLE MUST HAVE PRESSURE HIGHER THAN OPERATING PRESS.

AND LIQUID ENTHALPY LOWER THAN THE BUNDLE INLET ENTHALPY *

.. -> - .. .. .. ____ _J

---~--~~-~-~~~~--~-

CARD GROUP 2, FLOW CORRELATIONS READ IN UP TO FOUR SETS OF FRICTION FACTOR CORRELATION CONSTANTS THAT CORRESPOND TO THE SUBCHANNEL TYPES, FORMAT(l2F5.3).

Nl IS THE SUBCOOLED VOID CORRELATION OPTION. Nl=O, NO SUBCOOLED VOIDS. Ul=l, LEVY SUBCOOLED VOID CORRELATION.

N2 IS THE BULK VOID CORRELATION OPTION. N2=0, HOMOGENEOUS MODEL.

N2 = 1, MODIFIED ARMAND MODEL. U2=5, READ IN SLIP RATIO, FORMAT (5X,El0.5). N2=6, READ IH THE NUMBER OF TERMS AND COEFFICIENTS FOR UP TO A SIXTH ORDER POLYNOMIAL FUNCTION OF STEAM QUALITY, FORMAT I I-'

(I5,7El0.5). co CJ\

I N3 IS THE TWO-PHASE FRICTION GRADIENT MULTIPLIER OPTION. N3=0, HOMOGENEOUS. N3=1, ARMAND. N3=5, READ IN NUMBER OF TERMS J\ND COEFFICIENTS FOH UP TO A SIXTH ORDER POLYNOMIAL FUNCTION OF QUALPf FORMAT(I5,7El0.5).

NII IS AN OPTION TO INCLUDE A WALL VISCOSITY CORRECTION TO THE FRICTION FACTOR. IF N4= 1 J IT IS INCLUDED, OTimmnsE rrr IS NOT.

CAHD GROUP 3, AXIAL HEAT FLUX 'f ABLE READ IN Nl PAIR OF DATA FOR THE TABLE. EACH PAIR CONSIS'rs OF THE RELATIVE POSITION(X/L) AND TIIE CORRESPONDING ffi.i:LA'fIVE IIEJ\T FLUX (Local flux/AVERAGE li'LUX), EACH CARD ACCEPTS UP TO SIX PAIR OF DATA, }i'ORMA'f(l2F5. 3). Nl r.msr Im GREA'fER THAN ONE BUT NOT GTIEA'fER THAN THE P AHAME'l'EH MP.

-187- I I

Card Group 4 (Channel Data) Card (1)

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Required to be present when IPILE=l or 2 F9RTRAN READ list NG ROUP I FORTRAH FORMAT READ from subroutine I5 INDAT I

~~~~~~~~~~-----21 Variable Columns Description NGROUP 1-5 = 4 (To select Card Group 4) I I

I NOTE: Once this card is read in the new subroutine CARDS 4 is entered for the remaining Read statements and Data I processing of this Card Group 4.

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I -188-I Card (2)

I I Required to be present when NGROUP = 4 FORTRAN READ list Nl, N2, NGRID, HGRIDT, NODESF, I FORTRAN FORMAT NFUELT, NCHF, IMAP, ITEXT 9I4 I RP-ad from subroutine Variable i~I o umns 1-4 CARDS4 escr1ot1on

~1umoer- or channel types I N2 5-8 (max 15) see below)

Total number of channels I NG RID 9-12 in problera Number of grid positions

'I NGRIDT 13-16 Number of types of grid NODESF 17-20 Number of radial nodes on I NFUELT 21-24 the fuel for center temp. calculo Number of fuel types I NCHF 25-28 = O for no CHF calculations

= 1 for B&W2 CHF correlation I = 2 for W-3 correlation

=1

• I IMAP 29-32 to 4 to indicate method of

., ITEXT 33-36 presenting gap interconnection data (see Cards (9) below) number of cards to be read in next which will be printed out as a message. If ITEXT=O, no I lJOTE message cards are read in Channels are defined as being all of the same type if they I have the same geometry, rod dimensions and grids and only differ in their power. More precisely, Cards (4) and (5) given later which I define the geometry and grids must apply to all channels of the same type. In, for example, 1/4-core symmetry data, 1/4, 1/2 a.~d I whole channels would be of different types.

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-189-I I

Card (3) I Required to be present when ITEXT > 0 FORTRAN READ list TEXT I

FORTRAN FORI*1A'I1 Read from Subroutine 20A4 CARDS#

I Variable Columns I TEXT 1-80 The array TEXT (20) is read

~~d immediately printed in a DO I

loop from 1 to I TEXT. It is envisaged that a map of the channel nul"'.'.bering system could I be printed as an aide-memory in a large problem.

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I -190-I Card (4) 1* Required to be present Always (being !JG ROUP= 4)

FORTRAH READ list N,I,FRAC, AC(I), PW(I), PH(I)

I GAPS(I,l), DIST(I,l), DR(I),

PHI(I,l.), M I FORTRA~~ FORMAT READ from subroutine Il, I4, 8E9.3, I2 CARDS4 1*

Variable Columns _ Description I

I N 1 Selector for friction factor expression. If ~J=O reset to 1.

• 1 I 2 - 5 Any channel number, preferably the first of the channe 1 type being described.

I FRAC 6-14 Factor by which AC, PW, PH should be multiplied. Thus for 1/4 channel, one may give FRAC =

0.25 and AC, PW, PH the same as I for a whole channel.

AC 15-23 Channel flow area (in 2 )

I PW 24-32 Channe 1 wetted pe rime te r (in)

I PH GAPS 33-41 42-50 Channel heated perimeter (in)

Boundary gap dimensions (in)

DIST 51-59 Centroid-to-centroid channel distance (in). This is only required for a particular mixing correlation and may normally be given as zero.

DR 60-68 Rod diameter (in)

PHI 69-77 Number of rods in channel M 78-79 Fuel type: = 1 for rod,

= 2 for plate, Reset to 1 if M = O

-191- I Card (5)

Ii Required to be present If IWRID > 0 IIi FORTRAN READ list (CD (I.L), L=l, IWRIDT),

L=l, ;-.JGRIDT

'h'x.1"'<'(')

\- LJ 'I/

I FORTRAH FORI*IAT 16 ~E5.3 Head from subroutine CARDS4

'II- I 11 Variable columns  ::Jescriptions CD Spacer loss coefficients FXF Fraction of axial flow forced across each boundary. It is not expected that this would 1*

be used in reactor problems hence nominal value = O. O I If Nl (Card (2) ) is greater than one, cards describing IC channel and grid for channel type 2 will be given now, I

after these cards, the ones describing channel type 3 will be inputed and so on until the completion of the I 1n channel types.

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I -192-I I, Card (6)

I Required to be present Always I FORTRAN READ list FORTRAN FORMAT (Radial (I), I=l, NROD) 16 E5.3 I Read from subroutine CARDS4 I Variable Columns Description I RADIAL 1-70 Radial power factor for rod I which is located in channel I. This is defined *~

as the ratio of the rod power I to that of the reactor average power.

I, Notes:

I a) NROD is the tota1 number of rods, having set to lWHAi.'lL (total number of channels) which was its elf set to :*.r2 I (Card ( 2) )

• I b) If all rods have the same power, RADIAL (1) alone may be given a.11d is set negative. THis triggers setting (RADIAL (I);

I I=l, NROD) = 1.0 I

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-193- I I

Card (7)

I Required to be present FORTRAH READ list If ~~GRID > 0 (GRIDXL(L), IGRID(I),

I (I=l, iJGRID)

FORTRAiI FORMAT 8(E5.3, I5) I Read from subroutine CArt.DS4 I

Variable Columns Descritpion I GRID XL Relative location (z/L) wl1ere grids are located I

I GRID I

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Ii----~~~~~~~~~~

Card (3)

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'  ! Required to be present If Nl (Card(2) > 1 FORTnA:r READ list JB(I)

I FORTRAN FORMAT I Read from subroutine. CAP~S4 I..-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-'

I Variable Columns Description

• I JB 1-80 List of channels of Type 2 I  :'late s :

I The first set given is the list of channel numbers in Type 2.

The list is terminated by reading in a zero (or a blank space).

Hence, if the last channel number comes at the end of a card, a blanl{ card must follow in order to give the terminating zero *

..:t is safer to make a habit of punching a final zero. FollowinG Type 2, card(s) are read in for those cha."1.nels in Type 3, then Type 4 etc. UP to 111 Types.

lfote that since the channel numbers for Type 1 are not read in, it is more economical to *select '::'ype 1 as that with the major-ity of channels.

An internal consistency check is made ~1hen reading in JB (I)

• If a set includes the channel number (I in Card ( 4) ) for Type 1 or does not include that given for its own type in Card ( 4) ' an appropriate message is printed and the run terninated.

Ii' iH = l, the JB cards above are not given.

-195- I Card (9a)

Required to be present BWR case, no cards are given the channels are not connected) sinl :

only if IPILE = 1 (If IP::CLE = 2)

.C.

IHAP = 1 ( Card ( 2 ) )

FORTRAN READ list ICROSS, IDOWll I FOR.~RAH FORNA'I' 2I4 Read from subroutine CARDS4 I Variable Columns Description f

I ICROS 1-4 ID OWN 5-8

} see notes below 1*

11*

iWTES This option is only possible to use when the pattern of channel is recta."1.gular. If this is the case, I CROSS is the number of columns and IDOWH the number of rows. For I

example, in the case represented in figure 1, ICROSS should be 4 and IDOWN 3.

is 20.

The maximum value for IDOWN and ICROSS The channels are sequentially numbered by the computer and the channel boundaries set in the IK, JK arrays; the

• ti oreder is that used to illustrate the case of IMAP = 4

( Card ( 9 d) )

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I -196-I.

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I 1 2  :;7 4 I

• 1. J 6 7 3 I.

I 9 10 11 12 I

I Figure 1.

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• Rectangular Matrix of Channels I

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-197-I I

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\I 5 6 7 8 9

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FIGURE 2 Irregular Pattern of Channels I I

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I -198-I Card ( 9'IJ)

I Required to be present Where IPILE

.IMA.P = 2

=1 and I FORTRAN READ List ISTART IEND FORTRAN FORMAT 2I4 I Read from subroutine CARDS4 I Variable Columns Description I IS TART 1-4 First channel in each row Last channel in each rm-1 IEND 5-3 I lJotes:

One of these cards should be given for each row.

I  !-l'ote *that this method could not be used if there I were an insert blank channel in any row; for this case use IMAP = 3. The maximum value of IEND is I 20 and the maximura number of rows is also 20. If less than 20 rows are to be given, a blank card I

., (or one with two zero) should be given after the last row.

The computer numbers the channels and the boundaries I sequentially as illustrated in Figures 1 and 2.

Examples follow:

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-199-I For Figure 1 the following cards should be inputed: I I START IEND I

1 1

4 4

I 1 4 I 0 0

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For Figure 2 the following cards should be inputed: I I START IEND I 3

3 3

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i 5 I 4 4 0 0 I I

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-200-I Card ( 9 c)

I Required to be present When IPILE IHAP = 3

= 1 and I FORTRAN READ list (NAAP(L), L= 1,20)

FORTRAN FORHAT 20 I4 I Read from subroutine CARDS4 I Variable Columns Description

'I MAAP 1-80 The number of the cha'l.nels malcing up a row I. Notes:

One of these cards should be inputed for each row I (maximum 20 rows). The value o.f T:IAAP represents the channel number with a zero indicating no cha.'1.nel. If less than I

20 cards are to be used, the last should be all zeros (i.e., a blank card). The set of cards represents a map

~'l'hich 1: of the channel numbering system, control of the user.

is thus under the The boundary ordering is done by I the computer.

Examples:

I For pattern described in figure 1 1 2 3 4 I 5 6 7 8 11 12 I 9 0

10 0 0 0

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I For pattern described in ~igure 2 I 0 0 1 0 0 2 3 4 I 5 6 7 8 9 I 0 0

0 0 lJ I

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-202-I I

Card (9d)

II Required to be present When IPILE = 1 a.'1.d H1AP = 4

'I FORTRAlJ HEAD list (IK(L), JK(L), L = l,NK)

FORTRAN F.ORMAT 20 I4 I L.----------R_e_a r_o_u_t_i_r-_~e________________c_A_RD

__d__f_r_o_m__s_u_b__ __s_*_ii_____________________________.~

Variable Description I

ColUTILYlS IK

} See notes be low JK ifote s:

I IK, JK are the channel pairs defining each boundary in I turn; lJK = nur.rber of boundaries specified. The set of numbers are read in, 20 to a card, continuing on as many I

cards as necessary. They are terminated by a zero; if the final channel number is at the end of a card, the I,

zero must be given on the next card. (lfote, the value of I

?IK is not known at the time of reading in IK, JK;. it is set to the number of pairs read in). Thus, with H1AP = 4, I both channel and bou.'1.dary numbering are under tne control of the user. When listing the sub channel pairs, it is I

preferable to give the loVTer number first; this saves the I computer reversing the order.

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I -203-I Card (9d)

I Examples 1 I For case in figure 2:

11 2 2 3 3 4 2 7 3 8 4 9 5 6 6 7 7 8 8 Q 18 10 0 0 I

For Case in figure 1:

I 11 2 2 3 3 4 1 5 2 6 3 7 4 8 5 6 6 7 7

,, 5 9 6 10 7 11 8 12 9 10 10 11 11 12 0 0 I

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-204-I I

Card ( 10)

I Required to be present When IPILE = 1 I FORTRAH Read list JB (L), L = 1J FORTRAH FORMAT 20 I4 I Read from Subroutine

-L-~~~~~~~~~~~~~~~~~

CARDS4 I Variable Columns Description I JB 1-80 List the identification number of the channels making up each "half- I boundary", i.e. the bound-aries that are split by a line of symmetry. I Notes: I Always terminate with a zero. If there are no half boundaries, give a single card with a zero. The I

parameter FACTOR(K) is set to 1.0 for full boundaries 1-and 0. 5 for "half-boundaries".

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I -205-I.

Card (11)

I Required to be present When 2JODESF > 0 I FORTRA11 READ list (K FUEL(I), CFUEL(I),

fiFUEL(I), DFUEL(I),

I KCLAD(I), CCLAD(I),

RCLAD(I), TCLAD(I),

HGAP(I), I=l, NFUELT I FORTRAN FOill TAT 1

16E5.3 Read from subroutine CARDS4 I

I Variable KFUEL Columns 1-5 Descriotion Fuel thermal conduction BTU I ( hrf~°F )

CFUEL 6-10 Fuel specific heat I

BTU lb °F RFUEL 11-15 Fuel Density (lb/ft 3 )

DFUEL 16-20 Pellet Diameter (in) 1 KC LAD 21-25 Cladding thermal conduction BTU hrft °F

• 1 CLAD 26-30 Cladding specific heat BTU 1* RCLAu 31-35 lb °F Cladding density (lb/ft3)

I TC LAD 36-40 Cladding thickness (in)

HGAP 41-45 Fuel-cladding heat 2ransfer coefficient (BTU/ft hr°F)

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CAHD GROUPS 5, 6, 9, 10, 11 AND 12 ARE READ IN BY SUBROUTINE INDAT WITH THE FOLLOWING FORMAT:

CARD GROUP 5, SUBCHANNEL AREA VARIATION TABLE Di' THERE ARE NO AREA VARIATIONS, OMIT THIS CARD GROUP.

READ N2 VALUES OF RELATIVE LOCATION(X/L) WHERE AREA FAC~l'ORS ARE GIVEN FORMArr ( 12F5. 3)

• N2 MUST BE GREATER THAN mm BUT NOT GREATER THAN THE PARAMETER ML.

READ Nl SETS OF AREA VARATION FACTORS(LOCAL AREA/NOMINAL AREA).

EACH SET CONSIS'l1S OF SUBCHANNEL NUMBER AND N2 AREA VARIATION I l\J 0

FACTORS, FORMAT(I5/(12Ji'5.3)). Nl IS LIMITED BY THE PARAMETER MA. CJ\

I IF Nl IS ZERO, AREA VARIATIONS ARE DELETED FOR SUCCEEDING CASES.

N3 IS THE NUMBER OF ITERATIONS FOR INSERTING AREA VARATIONS.

IF N3 IS ZERO OR BLANK, N3 IS SET EQUAL TO 1.

CARD GHOUP 6, CAP SPACING VARIATION TABLE Ill' 'rIIERE ARE NO GAP VARIATIONS, OMIT THIS CARD GROUP.

READ N2 VALUES OF THE RELATIVE LOCATION(X/L) WHERE GAP li'ACTORS ARE GIVEN, Ji'ORMAT(l2F5.3). N2 MUST BE GREATER THAN ONE BUT NOT GREA'l'ER THAN THE PARAMETER ML.

READ Nl SETS 01" GAP SPACING l"ACWORS (LOCAL GAP /NOMINAL GAP).

EACH SET CONSIS'l'S OF THE ADJ AGENT SUBCHANNEL NUMBERS FOR THE GAP N2 GAP VARIATION l"ACrroRs, FORMAT( 2I5/( 12F5. 3)). Nl IS LIMITED BY THE PAHAMETEH MS. IF Nl IS ZEHO, GAP VARIATIONS ARE DELETED FOR SUCEED CASES.

CARD GROUP 9, CALCULATION VARIABLES RirnD IN DIVERSION CHOSSFLOW RESISTANCE FACTOR, TURBULENT MOMENTUM FACTOR, BUNDLE LENGTH(IN.),, POSITION FROM VERTICAL(DEGREES), NUMBER OF AXIAL NODES, NUMBER OF TIME STEPS, TOTAL TRANSIENT Tif.lE(SECONDS)

MAXIMUM NUMBER OF ITERATIONS, ALLOWABLE FRACTION ERROH IN FLOW Ji'ORM CONVERGENCE AND THANSVERSE MOMENTUM PARAMETER(S/L),

FORMAT(llE5.2,2I5,E5.2,,I5,4E5.2). IF THE NUMBER OF ITERATIONS, ALLOWABLE ERROR AND MOMENTUM PARAMETER ARE BLANK OR ZERO, THE PROGRAM USES 20,, 1.E-3, AND .5, RESPECTIVELY.

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(\)

Nl IS AN OPTION GIVING THE SPATIAL PRINTING INCREMENT. IF Nl=l, EVERY 0

--.1 I

STEP IS PRINTED. IF N2=2, EVERY OTHER STEP IS PRINTED, ETC. IF N

'.':EHO OR BLANK, THE PROGRAM SI:':'S Nl=l.

N2 IS AN OPTION GIVING THE TIME PRINTING INCREMENT AND IS SET UP THE SAME AS Nl ABOVE.

N3 IS A DEBUG PRINT OPTION. IF N3=0, NO_DEBUG INFORMATION IS PRINTED IF N3=1 A DEBUG PRINT IS MADE FOR EACH STEP OF THE CALCULATION. IT CAN GENERATE A LOT OF PAPER SO IT IS NOT NORMALLY USED.

CARD GROUP 10, TURBULENT MIXING CORRELATIONS Nl IS THE OPTION FOR SUBCOOLED MIXING CORRELATIONS. FOR ANY SELECTED VALUE OF Nl READ IN THE CONSTANTS A AND B, FORMAT(2F5.3).

THE OPTIONS ARE --

Nl=O, W/GS=A Nl=2, W/GS=A*RE**B Nl=2, W/GD=A*RE**B Nl=3, W/GS=D/AIJ*A*RE**B NOTE THAT BETA = W/GS WHERE W IS THE TURBULENT CROSSFLOW.

N2 IS 'rIIE OPTION FOR TWO-PHASE MIXING. IF N2=1, TWO-PHASE MIXING IS THE SAME AS FOR SUBCOOLED CONDITIONS. IF N2 IS GREATER THAN ONE READ IN N2 PAIR OF DATA FOR A TABLE OF TWO-PHASE MIXING DATA.

EACH PAIR CONSISTS OF THE STEAM QUALITY AND THE CORRESPONDING VALU OF BETA. N2 IS LIMITED BY THE PARAMETER MP. I ru 0

(X)

N3 IS THE OPTION FOR THERMAL CONDUCTION MIXING. IF N3=0, NO THERMA I CONDUCTION. IF N3=1, READ IN THE THERMAL CONDUCTION GEOMETRY FACTO FORMAT(F5.3).

CARD GROUP 11, OPERATING CONDITIONS READ IN THE OPERATING PRESSURE(PSIA), INLET ENTHALPY(BTU/LB)

OR INLET T~MPERATURE(DEG-F), MASS VELOC~TY(M-LB/HR-SQ-FT) AND AVERAGE HEAT FLUX(M-BTU/HR-SQ-FT).(6Fl0.0)

Nl IS THE INLET ENTHALPY OPTION. IF Nl=O, INLET ENTHALPY IS GIVEN. IF Nl=l, INLET TEMPERATURE IS GIVEN. IF Nl=2, READ IN THE

,-:~

INDIVIDUAL SUBCHANNEL INLET ENTHALPIES, FORMAT(l2F5.0). IF Nl=3, READ IN THE INDIVIDUAL SUBCHANNEL INLET TEMPERATURES, FORMAT(l2E5.0)

N2 IS THE INLET FLOW DISTRIBUTION OPTION. IF N2=0, THE SUBCHANNELS ARE GIVEN THE SAME MASS VELOCITY. IF N2=1, THE INLET FLOW IS DIVIDED TO GIVE EQUAL PRESSURE GRADIENT IN THE SUBCHANNELS. IF N2=2, READ MASS VELOCITY FACTORS FOR EACH SUBCHANNEL, FORMAT(l2E.50).

N3, N4, N5 and N6 ARE OPTIONS FOR TRANSIENT FORCING FUNCTIONS. IF' ANY OF THESE OPTION NUMBERS ARE ZERO OR BLANK, THE CORRESPONDING FORCING DATA IS NOT READ AND IS EXCLUDE FROM THE CALCULATIONS. EACH OF THESE NUMBERS GIVE THE NUMBER OF PAIRS OF TABULAR DATA TO BE READ FOR EACH FUNCTION. ALL DATA ARE READ AS PAIRS OF TIME (SECONDS)

AND RELATIVE VALUE, FORMAT (12E5.0).

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N3 IS THE OPTION FOR REFERENCE PRESSURE VERSUS TIME. 0

\D N4 IS THE OPTION FOR INLET ENTHALPY OR TEMPERATURE AS A FUNCTION OF I TIME DEPENDING ON THE OPTION FOR INLET ENTHALPY OR rrEMPERATURE.

N5 IS THE OPTION FOR INLET FLOW VERSUS TIME.

N6 IS THE OPTION FOR HEAT FLUX VERSUS TIME.

CARD GROUP 12, OUTPUT DISPLAY OPTIONS Nl IS AN OPTION FOR PRINTING ANSWERS.

Nl=O, PRINT SUBCHANNEL DATA ONLY.

Nl=l, PRINT SUBCHANNEL DATA ANC CROSSFLOWS.

Nl=2, PRINT SUBCHANNEL DATA AND FUEL TEMPERATURES .

.J Nl=3, PRINT SUBCHANNEL DATA, CROSSFLOWS AND FUEL TEMPERATURES.

N2 IS AN OPTION FOR SUBCHANNEL DATA PRINTOUT. IF N2=0, ALL SUBCHAN DATA ARE PRINTED. IF IT IS CALLED FOR BY Nl. FOR N2 GREATER THAN Z READ IN THE SUBCHANNEL NUMBERS FOR WHICH RESULTS ARE TO BE PRINTED FORMA'l 3612).

1

(

N3 IS AN OPTION FOR FUEL TEMPERATURE PRINTOUT. IF N3=0, DATA FOR ALL RODS ARE PRINTED IF CALLED FOR BY Nl. FOR N3 GREATER THAN ZERO, READ IN N3 ROD NUMBERS FOR WHICH TEMPERATURES ARE TO BE PRINTED, I~ORMAT ( 3612). IF CHF DA'rA IS CALLED FOR BY INPUT OPTION IT IS PRINTED FOR EACH SELECTED ROD PLUS A

SUMMARY

TO IDENTIFY THE ROD AND CHANNEL WITH THE MINIMUM CHF RATIO. I I\)

I-'

0 N4 rs AN OPTION FOR FUEL NODE PRINTOUT. IF N4=0, TEMPERATURES ARE I PRINTED FOR EVERY NODE. FOR N4 GREATER THAN ZERO, READ IN N4 NODE NUMBERS TO BE PRINTED, FORMAT(3612).

TO START A CALCULATION, READ A BLANK GROUP CONTROL CARD.

TO STOP THE CALCULATIONS, AFTER FINISHING A CASE, READ A BLANK CASE

• • • • • END OF INPUT INSTRUCTIONS ****

UNITS - ALL COMPUTATIONS ARE DONE USING FT, LB, SEC, BUT AND DEG-F.

UNIT CHANGES FOR INPU'l AND OU'l PUT ARE DONE IN THE PROGRAM.

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I -211-I I APPE?1DIX 12 I New INPUT DATA Presentation I

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I -2lla-co I Card(s) Type:

Required to be pr.esent:

Problem Array Size Always I FORTRAN READ list: NAP NFS FORTRAN FOIU*fAT: 215 I Read from Subrout:i.ne: IND AT I

., Variable NAP Columns 1-5 Format IS Description Number of axial positions u~ed forinputting the heat flux shape (sets size of matrix, NAP > Nl I given on card CS)

NFS 6-10 15 Number of flux shapes input (sets I* size of matrix, NFS > JFS given on card .cs)

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,. -212-1l~~~~~~~~~~~~~~~~

Card(s) Type Cl Problem Array Size

., Required* to be present Always FORTRA.~ READ list:

• MC MG MN MR MX I FORTRAI.~ FORMAT: lOIS Read from S~broutine: INDAT

-I --------------~

-I Variable Columns Format* Description CG MC. 1-5 IS ~No. of channels (NCHANL) in pro-I. ..

• blem. NCHANL is set from NTHEOX on cards CS-C7, or in the original COBRA format, in Card Group 4.

I MG 6-10 IS ~ No. of gap inte=connections (NK) between channels i~.problera. If this is net known~ MG=Z*MC is usu-I* ally adequate but should be checked later.* For a BWR .. MG mav be given as zero, ~hen it is reset ~o l in I CORE.

MN 11-15 *IS ~ No. of fuel nodal points in problem.

I This*should be~ (~ODESF+l} on Card Tl. If MN is given as zero, it is reset. to 1 in CORE.

I MR 16-20 IS ~ No. of rods (NRCTI) in problem ..

For PWR and BWR, ~;;{QD=NCHANL, her~ce I* 21-25 IS MR may be gi.ven=MC.

~- No. of c.xial stati_cns in proble:.t. -

It may be given as NDX (Card Cll)

I as it is increased by l after reading in.

innedia~ely I Notes (1) MC to MX are used to set the array sizes in the dynamic sto-I (2) rage, hence they should be set too big rat:her than too smalls Note that MC ~o ~a are given in alphabetic~l order.

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I -212a-I Card(s) Type: Cla Required to be present:

CHF Correlation Always I FORTRAN READ list: NCHF JBXC JWRBl JGRID FORTRAN FORMAT: 4IS I Read from Subroutine: IND AT I Variable Columns Format Description I NCHF 1-5 IS CHF correlation indicator

=0 for no CHF calculations I =1 for B&W correlations

= i for Westinghouse correlations I

JBXC 6-10 IS B&W indicator.

I =0 for B&W-2 correlation

= 1* for BXC correlation I

Jvnun 11-15 IS Westinghouse indicator I = 0 for W-3 correlation I = 1 for WRB-1 correlation JGRID 16-20 15 W-3 spacer factor indicator I = o*for no grid factor

=1 I for L-grid. factor

= 2 for R-grid factor I

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I -212b-I Card(s) Type: Clb W-3 Spacer Factor Parameters Required to be pr~sent: Only if NCHF = 2. JWRBl = 0 JGRID :f: 0 I FORTRAN READ 1 if; t: XKS TDC I FORTRAN FORMAT:

Read from Subroutine:

2Fl0.S IND AT 1 Variable Columns Format Description I XKS 1-10 Ft0.5 Axial grid spacing coefficient (k. )

s I TDC 11-20 Fl0.5 Thermal diffusion coefficient (TDC)

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I -212c-I Card(s) Type: Cle Required to be present:

WRB-1 Correlation Parameters Only if NCHF ,;,, 2 JWRBl = 1 I FORTRAH READ list: GSP PF FORTRA.i.~ FORMAT: 2Fl0.5 I Read from Subroutine: INDAT I Variable Columns Format Description I GSP 1-10 no;s Grid ~pacing (in)

PF 11-20 Fl0.5 Performance factor I

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I -212d-I Card(s) Type: Cld Identification of the Hot Channel Always Required to be p~esent:

I FORTP.AN READ list: IHC FLOARE FORTP-AN FORHAT: IS, FlO.S I Read from Subroutine: IND AT

-*1 Variable Columns Fonnat Description I IHC 1-S IS Channel number which.is the hot channel I FLOARE 6-15 Fl0.5 Nominal flo~ area of the hot channel (in )

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I -212e-I Card(s) Type: Cle.*

Required to be pr_esent:

Miscellaneous Data Always I FORTRAN READ 1 is t : FNT XOINCH DAMPNG DNBRX HLEN FORTRAN FORMAT: 5Fl0.5 I Read from Subroutine: IND AT I Variable Columns Format Description I FNT 1-10 Fl0.5 Fraction of heat generated in the fuel and cladding I

• XOINCH 11-20 Fl0.5 Axial elevation at which active fuel starts (in)

I DAMPNG 21-30 Fl0.5 Damping factor to aid convergence of th~ flow solution (0.0 < DAMPNG I < 1.0)

DNBRX 31-40 ,Fl0.5 Multiplier on all DNBRs I Heated Length (ft)

HLEN 41-50 Fl0.5 I

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I -213-Card(s) Type C2 Maximuia Running Time I:.--* Required* to b*e present Always I FORTRAN READ list:

• MAXT FORTR.2\N FORMAT: IS, 6El2.6 I Read. from Subroutine: IN DAT I Variable Columns Format Description CG I MAXT 1-S !S is 2000.

Maximum Running Time, Nominal value c 0

N I .. T R

0 L*

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-214-I Card(s) Type I

C3 Case Control Card Required.to be present Always I FORTRAN READ list: I PILE KASE Jl TEXT FORTRAN F0&."1AT: Il, I4, IS, 17A4 I Read. from Subroutine: INDAT I

I Variable I PILE Columns 1

Format II Description

= O for simplified method CG c

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= 1 for PWR 0

= 2 for BWR The value is unimporta.~t if Card N

T I

Group 20 is selected since it is R overwritten on card Tl. 0 L I KASE 2-5 I4 Run Identification iJumber -- as in COBRA IIIC.

If > O, calculation continues; if I

~ , calculation stops.

Jl 6-10 I5 Printing option for standard COBRA I

output--as in COBRA IIIC.

= O print only new input

= 1 print entire input

= 2 print only operating conditions I

• This option is only effective if NOPRIN = O, i.e., Nl =Don card C4 I TEXT 11-78 Alphanumeric information to identify Case.

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I -215-

~*

Card (s) Type C4 Required.to be present Select Card Group 20 Always I FORTRAN READ list: NG ROUP Nl N2 N3 N4 NS N6 FORTRAN FORMAT: tIS I Read. from Subroutine: INDAT I

I Variable Colur.ms Format Description CG I NG ROUP 1-5 I5 = 20 Nl 6-10 I5 Printing trigger, NOPRIN, set c I to NL Nl=O, standard COBRA IIIC printing obtained as well as 0

N as "new" printout. Nl=l, standard T I N2-?~6 11-35 I5 COBRA printing suppressed.

Leave blank R

0 L

I Notes:

• I ( 1) If NGROUP = O, this acts as a trigger to stop reading Input Data and to start the hydraulic calculation (.eog., after I card T30).

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-216-card(s) Type cs Channel Map parameter I

Required.to be present*

Always I FORTRl-.l'i READ list: IMAP . NDlX NDZX FORTRAN FORMAT: 14IS I Read. from Subroutine: CARDZO I

Variable Columns Format Description CG I IMAP 1-5 IS Selects method of reading channel into array NTHBOX (NDlX, NDZX).

!MAP=l, Z or 3 I

NDlX 6-10 IS I

NDZX 11-15 IS J . Size of array NTIIBOX, maximum values of each are ZS.

I If IMAP = 1 2 3 I

Go to Card cs C6 C7 I*

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I - -217-I.

I The channel numbering system is con~ained in the

• 1 array NTHBOX (NDlX, NDZX) with a zero for each non-channel.

The array is later used to define the interaction between I adjacent channels. Thus a channel map:

I l I. 2 3 4 5 6 7 8 I 9 I

would be represented in NTHBOX (S, 4) as

.1 0 0 1 0 I 0 2 3' 0 0

0 I 4 s 6 7 8 -

0 0 9 0 0 I

1£ IMAP*l, there are assumed to be NDlX :* ND2X channels I numbered sequentially along each row, and column by columnj I to give a rectangular matrix.

gives a channel map:

Thus IMAP*l~ ND1X=4, NDZX=3 I 1 2 3 4 I s. 6 7 8 9 10 11 12

'I For IMAP=Z, 3 more complicated channel maps may be specified.

-218- I card(s) Type C6 Channel Map I Required.to be present* Only if IMAP=2 FORTRAN READ list: * !START IFIN I FORTRAN FORMi'\T:

Read. from Subroutine:

1415 CARDZO NDZX Cards of this type read.

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Variable Columns Format* Description CG I

!START 1-5 IS see below IS I

!FIN 6-10* II A total of NDZX cards of this type are read sequentially, one I

for each row of the channel map. Each card gives the start and finish of the row. For example, ISTART=3, IFIN=6 would imply a I row . 0 0 (N+l) (N+Z) (N+3) (N+4) o a etc. where channel N was the last channel in the previous row. I For IMAP=Z, ND1X=7, NDZX=4, cards 3 3 I

3 1

6 7 I 2 2 would represent a channel map I 1 *I 2 3 4 5 6 7 8 9 10 11 12 I 13 I

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-219-I card{s) Type C7 Channel Map

1. Required.to be present Only if IMAP=3 FORTRAN READ lis.t: ( (NTHEOX (NDl, ND2), NDl=l, NDlX), ND2=1, 1- FORTRAN FORMAT: (1415)

ND2X)

'I Read. from Subroutine: CARD20 I Variable Columns Format* Description CG I NTHBOX 1-70 14!5 Channel identification number I If ND1X>l4, the remaining numbers (i.e., 15-NDlX) are read on a corntinuation card. Note NDlX must not exceed 25. Each row of I NTHBOX must start on a new card.

I For IMAP=3, NDlX= 7, NDZX=4, cards.

I :Q 0

0 0

l 2 3 4 s 6 7 8 9 10 11 12 I 0 13 I would give the same channel map as that illustrating IMAP=Z (see card C6).

I IMAP=3 could be used, either to specify a particular numbering system or wheri there are two channels in the same row separated by a I "zero."

I In the simplified method, (i.e. IPILE=O) *cases as the one represented I below may be required to be used. To input this kind of array only IMAP=3 is adequate*. **lfihe cards needed are illustrated in the I figur*e below ..

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-220-1 2 3 4 6 7 8 9 5 10 11 12 13 14 16 17 18 19 15 20 21 22 23 24 25 26 27 28 IMAP=3, ND1X=6, ND2X=6 and 1 2 2 3 3 4 5 6 7 8 9 10 5 11 12 13 14 10 15 16 17 18 19 20 15 21 22 23 24 20 25 26 26 27 27 28

I -221-I Card(s) Type: C8 Require& to be present:

Indicators for Axial Flux Shapes Always I FORTRAN READ list: Nl JNR* JFS AFLUX FORTRAN FOP.i.'1AT: 315, ElO. S I Read from Subroutine: CARD20 Variable Columns Format Description I Nl 1-S IS Nl=O; t~igger to read average nodal fuel powers after rest of data (Cards Cl2-14). NAX set to 0, IQP3 set to I 0.

Nl=l; trigger to read average nodal fuel and coolant powers after rest of da~(Cards Cl2-14). NAX set to I 0, IQP3 set to 1.

Nl_.:2; number of axial positions used I for inputting the axial flux.shapes given on ca'I'd C9. Maximum value of N1=30. NAX set to Nl, IQP3 set to 2.

I JNR 6-10 IS Total number *of rods input JFS 11-lS IS Number of axial flux shapes input I AFLUX 16-25 El0.5 (l~JFS <6)

Core average heat flux in MBtu/hr-ft 2

• If Nl=O or 1, the value of AFLUX is I irrelevant and may be given as zero.

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I -22la-I Card(s) Type:

Required to be present:

C8a Numbering Scheme for Axial Flux Shapes Only if Nl>l and JFS>l I FORTRAN READ 1 is t : (NRFLX(I), I= 1, JNR)

FORTRAN FORMAT: (1415)

I Read from Subroutine: CARD20

-I Variabl~ Columns Format Description I NRFLX 1-70 14I5 Flux shape number which is aP.plicable to each rod. The flux.shape numbers are input in the same order as the rods I are input. (l~NRFLX<6)

I NOTES:

(1) Card C9 allows the user to input from 1 to 6 *axial flux shapes. These flux I* shapes are numbered from l to 6, and each rod is assigned a particular flux shape via the numbering scheme provided on card C8a. The first yalue of NRFLX would be the flux shape number applicable to the first rod, the* second value of NRFLX would I be flux shape number applicable to the second rod, etc.

(2) If JFS = 1, then all the rods are .internally assigned the first flux shape.

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I -222-I Card(s) Type:

Required to be C9 pr~sent:

Axial Flux Shapes Only if 1h>l I FORTRAN READ 1 is t: (YFLUX(I), (AXFLUX(J), J=l,JFS), I=l;Nl)

FORTRAN FORMAT: 7Fl0.5 I Read from Subrou.ti.ne: CARD20 I Variable Columns Format Description YFLUX 1-10 Fl0.5 Relative axial position, X/L (O. 0<,YFLUX<l. 0)

AXFLUX 11-20 Fl0.5 Corresponding relative flux value for the first axial flux shape AXFLUX 21-30 FlO.S Corresponding relative flux value I for the second axial flux shape AXFLUX 31-70 4Fl0.5 Corresponding relative flux values I for the third, f~~rth, fifth, and sixth axial flux shapes I

I I NOTE:

First relative position must be 0.0, and the last relative position must be 1.0.

I I

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I

-223-I-- Card(s.)' Type ClO Rod Power Factors Required.to be present* Only required if Nl on Card C8~2 I FORTRAN READ li s*t: * (RADIAL (I), I=l, NCHANL) 1* FORTRAN FORMAT: (14ES. O)

Read. from Subroutine: READIN/CARDZO I *.

~

Columns Format Description CG Variable I 8 RADIAL 1-70 14E"S ** 0 Relative Rod Power (local/average)

I in problem (~MC in Card Cl)

• It is N.CHANL = No. of* channels set to the highest value of the channel map array I NTH BOX see cards CS-C7.

I Note In the simplified method (IPILE7Q) some subchannels are lumped together I to create .one channel, ~hile oth~rs are treated as individual sub channels, (see figure below). For those_e~ery channel can be visualized as having I only .o~e rod that generates the whole power of the channel. In order to reduce the Input Data the power given.to such a channel for its rod is sp~cified here, while rods that share their power with several .

channels, will be described in Card T5a.

I This system of *entering the Data, reduces the cards required in the old presentation (do not forget that more than 150 channels can be used I and only a few of them will be real sub6hannels) and only introduce the restriction that the lumped channels need to have the same identifi-I cation number as its rod ..

I The following example clarifies all these points:

p.

I

-224-I l=channel 2 3 I 0-l=rod 02 03 I

I 4 13 .~ Dr 5"-

5 6 9

0-I

b 7 I "'\ I 04 9 7 B" \

"\ T=i /

8 t"-..°fh ~ .... 17 I

10 11 12 0 10 I

0 0 11 12 I

I I

For this case, card ClO should have the actual relative rod power for channels 1, 2, 3, 4, zero for 5, 6, 7, 8- and the actual values for 9, 10, 11, and 12.

I The power given to channels 5, 6, 7 and 8 from rods 13, 14, 5, 6, 7, 8, I 15, 16, and 17 will be specified later in card T5a.

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I

-225-I"'* Card(s) Type Cll Mrscellaneous data Required.to be present 1 Always I FORTRAN READ list:

• FORT.R.:"\N FORMAT:

Read from Subroutine:

Z NDX NDT TTUIE (ES.O, 2IS, lOES.O)

CARD20 I

Variable Colu:m.ns Format* Description CG I

z 1-5 ES.O Channel length (in.) 9

. Nnx* 6-10. IS Number of axial intervals 9 I NDT 11-15 IS Number of time steps 9 NDT=O; steady state only I NDT)O; steady sta~e + transient TT I ME ES.O Total duration of transient (sec) 9 I 16-20 The length of each time step is set to TTIME/NDT

• I I

I I

I r

I  ! '

I, i

I

- -- --------- ------** *----*--* - **------ ----*--- *------*. -*-*--- ,.~

-226-

• Card ( s) Type I

Channel Indicators

_,,,* Required* to be present Tl Always I FORTRAi.~ READ list:

• IPILE

• NCTYP NGRID NGRIDT NODESF NFXF FORTRAN FOI'....-.!AT: (14I S)

I Read. from Subroutine: CHAN I Variable Columns Format* Description CG I I PILE IS Iteration trigger=O for.simplified method-* ~1

=1 for PWR, =2 for BWR NCTYP IS No. of channel types to be read

• in; controls reading of cards T2-T4.

NGRID 11-lS IS No. of grid positions (maximum=lO)

NGRIDT 16-20 IS No. of grid types (maximum=S)

NODE SF 21-ZS rs No. of fuel nodes

• NFXF 26-30 IS No. of "forced flow" in use; leave blank types. Not I

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I -227-I card(s) Type T2 Channel Data for Type Y t Required.to be present*

FORTRAN READ lis-t:

FORTRAN FORMAT:

Always N J . FRAC (215, SES.O)

GAP HNR Dm. A B C D Read. from Subroutine: CHAN I

I Variable Columns Format Description CG N IS Friction Indicator to select fric- 4 I tion factor for c-h..a.nnel (seeTlO).

Nominal value=l, zmaxirnum=4.

I J 6-10 IS Indicator to defi~~ A, B, C, D be-low (=l or 2)

FRAC 11-15 ES.O Amount by which cfuannel area, wetted I *.J and heated perimetiers and number of

• heated rods are t~ be multiplied (see below).

I GAP 16-20 ES.O Effective rod gav ~or interconnec-tion between chan.m.els (in.)

• If IPILE=O 4

this may be given as zero.

I

,. HNR DR 21-25 26-30 ES.O ES.O No. of heated rod's in fuel asseJI!,bly.

Diameter of heate~ rods (in.)

8 8

If J=l:

I A 31-35 ES.O Channel area cinZ] 4 I B-C 36-40 41-.45 ES.O ES.*O Channel Wetted pe'r*imeter (in.)

Channel heated perimeter (in.)

4 4

I

• D 46-50 ES. 0- Not used--leave hTuank I If J=2:

A 31-3S ES.O No. of unheated (e.g., control) rods t* B 36-40 ES.O Diameter of unhea~ed rods (in.)

c 41-45 ES. 0 Width of square a:ssembly (in.)

f ,

D 46-50 ES.O Radius of channe~ corners (in.)

I

-228-I I

Notes I (1) In COBRA IIIC., individual cards are read for each chan-nel and rod. For PWR and BWR smeared assemblies, considerable I

simplification is possible because (a) there is a one-to-one I

correspondence between channels and rods, hence the data may be given together, and (b) many channels have identical geometries, I hence one may give a typical geometry and specify to which chan-nels it applies.

I I

(2) Channels are of the same tyP.e if they a-ire described by the same data on cards T2, T3. I (3) Cards T2, T3, T4 are read sequentially in a DO Loop I

I=l, NCTYP. Channels making up Types 2, NCTYP are* specified on card T4. The unspecified channels are taken to be of I

Type 1, hence for economy, Type 1 should be defined as that I which contains the majority of the channels.

I (4) The channel area and perimeters may either be given directly (J=l) or calculated from the dimensicns of the assem-I bly (J=2). I (5) These parameters are multiplied by FRAC. Thus, if a I line of symmetry divides a channel -so that it is a half-channel, the data for a whole channel may be given and FRAC set to 0.5.

I

-,)

_, Alternatively, data for a single channel may be given and FRAC I

I

I*

-229-set to (say) 4.0 to obtain the parameters for a smeared I group of 4 channels. If FRAC is given as zero, it is reset I to l. O.

I (6) GAP is the "effective 1

' gap between assemblies. For no internal resistance to mixing within an assembly, GAP could I be considered to be the gap between individua.l rods

• the num-I ber of gaps. This would be reduced acccTding to the internal resistance ~ode! used.

I (7) Next card read is:

I NCTYP=l NGRID > 0 Card T3

=0 I NCTYP>l; NGRID Card TS I=l (i.e., first type)

I NGRID > 0 Card T3 NGRID =0 Card T2 for I=2 I NCTYP>l: I>l (i.e.,* subsequent types]

I NGRID > 0 NGRID =0 Card T3 Card T4 I

I*

I _}

I I

-230-

• I Card(s) Type T3 Grid Data for Channel Type I I Required.to be present Only if NGRID>O

PORTRAH READ list: (CDG(L),L=l, NGRIDT) I FORTRAN FORMAT: (14ES.O) I Read. from Subroutine: CHAN

• I Variable Columns Format* Description CG I

CDG 1-70 14ES. 0 Single phase grid coefficient for each grid type.

7 *1*

I I

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I

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I 1.

I

-231-I card(s) Type T4 Channels making up Type I Required.to be present Only if V>l I FORTRAN READ list: (JB (L), L=l, N)

FORTRAN FORMAT: (1415)

Read. from Subroutine: CHAN I*

I* Variable Columns Format* Description CG JB 1-70 IS Channel Identification Number for

'I Typ~ I ..

I Notes:

(1) The channels of Type I are listed on one or more cards. A complete card is read and the numbers up to the first zero are I taken as the relevant channels. The zero (or blank) must be given since it acts a*s a trigger, hence if the last channel number is at the end of a card, a blank ca.rd must follow to supply. the termina-I* ting zero.

(2) Next card read is:

I

,. I

• NCTYP I < NCTYP Card TS Card T2

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I

-232-I Card(s) Type TS Grid Positions I Required.to be present Only if NGRID)O I

FORTRAN RE.AD lis*t: (GRIDXL(I), !GRID(!), I=l, NGRID)

FORTRAN FQffi.1AT:

Read. from Subroutine:

( 7 (ES

• 0 , IS) )

CHAN I

I Variable Columns Fonnat Description CG *I GRID XL 1-70 ES.O Fractional distance up channel (x/L) 7 at which each grid is situated, i.e.,

O~GRIDXL~l.O '

1*

-tGRID 1-70 IS Grid Type; the coefficients for each type of grid were read by T3.

7 I I

1.

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• I

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I 1-1.

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-233-I I Card(s) Type T5a Rod Indicators Required to be present: only if IPILE=O I FORTRAN READ list: NNll, NN22, NN33, NN44 I FORTRAN FORMAT Read from Subroutine:

(415)

CHAN I Variables Columns Format Description CG I NNll NN22 1-5 5-10 I5 I5 Cards of rod layout data to be read Total number of rods 8

8 I NN33 10-15 I5 Number of radial fuel nodes including the cladding 8

I NN44 15-20 I5 Total number of fuel types 8 I

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-234- I Card(s) Type T5b Rod layout information Required to be present: only if IPILE=O and NNll > 0 I FORTRAN READ list: N, I, DR(I), RADIA(I), (LR(I,L), PHI(I,L), ,.

L=l,6)

FORTRAN FORMAT (Il, I4, 2E5.0,6(I3,E7.0))

Read from Subroutine: CHAN I Variables Columns Format Description N 1 Il Fuel rod type (1)

I 2-5 I4 Identification number of the rod I

DR(I)

RADIA(I) 6-10 11-15 E5.0 E5.0 Rod diameter (in)

I Relative rod power (rod power/average rod pow,f{

(2 ) [LR ( I, L) I3 Adjacent channel number ~

PHI(I,L) E7.0 Fraction of the rod power to that channel I

Then one card for every rod considered is required.

1*

I I

I (1) N=l indicates rod fuel 1*

N=2 indicates plate fuel (2) This block is repeated 6 times (L=l,6)

I I

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1* -235-I Card(s) Type T6 Fuel temperature data Required.to be present Only if NODESF)Q I FORTRAN READ list: KF(I), CF(I), RF(I), DF(I), KC(I), CC(I),

C(I), TC(I), HG(I), I=(l,N~U4)

II FORTR.t'\N FOR!-Lr..T: . (14ES. 0) ..

Read. from Subroutine: CHAN I

"' Variu.ble I Columns Format* Description CG

,. KF 1-5 ES. 0

• Fuel thermal conduc~ivity (Btu/hr ft °F) 8 s

CF 6-10 . ES.O Fuel specific heat (Btu/lb ~)

1* . RF 11-15 ES.O Fuel density (lb/£t 3 ) 8 DF *16-20 ES.O Pellet diameter (inch) a I KC 21-25 ES.O Clad thermal conduc~ivity (Btu/hr 8 ft "F)

I

,, cc RC 26-30 31-35

• Es. 0 ES.O Clad specific heat Clad density (Btu/lb °F)

(lb/ft 3) 8 8

TC 36-40 ES.O Clad thickness (inch) 8 I HG 41-45 ES.O Fuel-to-clad heit transfer coef- 8 ficient (Btu/ft hr~)

I I

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-236-

.I r--~~~~~~~~~~-.1 Card(s) Type T6a Effective rod gap for interconnection between channels (in)

Required to be present: Only if IPILE=O FORMAT READ list: (GAPREC(I),I=l,NK) where NK is the total I number of gap interconnections FORTRAN FORMAT: 14E5.0 I L---R_e_a_d__f_r__

om___s_u_b_r_o_u_t_i_n_e__: ___________c_H_A_N__________________________________________,~

Variable Columns Descriotion GAPREC 1-70 Effective rod gap for interconnection between channels (in)

I Notes I

In order to give to each boundary its gap these gaps should be inputed I in the same order as the boundaries are established. Then a few words are required to know how the boundaries are established. I I

For the following case the boundaries are established for the code as follows: .,

1*

I I

I I

I

• t

I -237..:.

-I

,I 1

I 2 I 4 5 I 3 7 8 6

.1*

I 9

I I

I Boundary number I . 1 2 34 5 6 7 8 9 10 11 12 13 14 I Pair of channels making up each boundary 1-2 1-3 2-4 2-5 3-4 4-5 5-6 4-7 5-8 3-7 7-8 8-6 I 7-9 8-9 I and in general the boundaries are established by going from

,. lef.t to rig..11t in each row two consecutive rows.

and frora top to bottom between I

I

I -237a-I Card(s) Type: T6b Require& to be present:

Indicators for Gap Coefficients Only if !PILE = 0 I: FORTRAN READ list: KXK IOIB FORTRAN Fon.MAT:

I 2!5

-, Read from Subroutine:

Variable Co lum.T'ls Format CH.AN Description I K.XK 1-S IS Number .of cross flow resistance coefficients input

• a v*

KXB 6-10 IS Number of mixing coefficients input I*

I I NOTE:

I KXK and KXB always equal 1 or the number gaps input on card T6a. If KXK equals 1, then the crossflow resistance coefficient input on card Tl7 is applied to all the gaps. If KXK equals the number of gaps, then individual crossflow resistance coefficients are input using card T6c. Simi+arly, if KY.B equals I 1, then the mixing coefficient, ABETA, input on card T9 is applied to all the gaps. When KXB equals .the number of gaps, individual mixing coefficients can be input using card T6d.

• I I

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I -237b-I Card(s) Type: T6c Required to be present:

Crossflow Resistance Coefficients Only i f KXK>l I FORTRAN READ list: (XFLOW(I) , I = 1, KXK.)

FORTHAN FORMAT: (14E5.0)

I Read from Subroutine: CHAN I Variable Columns Format Description I XFLOW 1-70 14ES.O Crossflow resistance coeffic.i.ents I

I I

NOTE:

I The number of crossflow resistance coefficients input must equal the number of gaps input on card T6a. The order in which the resistance coefficients I are input corresponds to the order in which the gaps are input.

I I

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1.

-237c-Card(s) Type: T6d Mixing Coefficients Required to be present: Only if KXl3 ~l FORTR.!\N READ list: (XEETA(i), I= 1, KXB)

FORTRAN FORMAT: (14ES. O)

I Read from Subrouti.ne: CHAN Variable Columns Format Description XBETA 1-70 14E5.0 Mixing coefficients I

I I NOTE:

The number of.mixing coefficients input must equal the number of gaps input on card T6a. The order in which the resistance coefficients are input corre-I sponds to the order in which the gaps are input.

I l 1 I

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-~-

I -238-I Card(s) Type Required.to be present T7 PWR "Half-Boundaries" Only if IPILE=l I FORTRlu~ READ list: * (II(L), JJ(L), L=l, N) where II(N)=O FORTRl\N FORMAT: (1415)

I Read. from Subroutine: CHAN 1 variable Columns Format* Descrintion CG.

1 II 1-70 IS } .

II(L), JJ(L) are th~ channel .iden-tification numbers ~hich define the JJ I "*

1-70 IS °Lth "half-boundary."

I . Notes:

(1) A "half* bounda1*y 11 is one cut by a line of symmetry*. In the example below the channel pairs defining the half-boundaries are I

• 1 and 4 , 4 and 6 *

~ *2 1 I 3 I '4 I

5 I. .

I

~

I a*:.*

(2) The list of. "half-boundaries" is terminated by a zero. If the I list finishes at the end of a card, a bi'ank card should follow to provide the ~era-trigger.

(3) If there are no half-boundaries, give a blank card.

I I

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1* -239-I Card(s} Type TS l~draulic Model Indicators Rcquired:to be present I FORTRAN READ list:

• Always Nl N2 N3 N4 NS N6 N7 N8 I FORT Rk'l FO R~AT: (14IS)

Read. from Subroutine: MODEL I

Variable Columns Format I Nl 1-S IS Description Mixing Indicator CG I N2 6-10 IS Sin-gle Phase Friction Indicator N3 11-15 IS Two Phase Friction Indicator I -N4 16-20 IS Void Indicator NS 21-25 IS Inlet Flow Indicator I N6 26-30 IS Parameter Indicator I N7 NB 31-35

• 36-40 IS

. IS Iteration Indicator Physical Property Indicator

1. . N9

~ "' *4

'41-45

- I5 **-- Coupling parameter -in**-the_ .. _____ --- -- - -

mixing term of the energy*

Notes: equation I (1) If all Nl-N8 given as zero (i.e.~ blank card) a preset hydraulic model is obtained and the next card read is T20. If I any are g1ven positive, the appropriate part of the model may be changed by giving extra card.(s).

I (Z) The preset model.is defined in the card-descriptions fol-lowing for the appropria~e Indicator=O.

I I

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-240- I Card (s) Type T9 Required.to be present Mixing Model I

Only if Nl (on TS)> 0 FORTRAN READ list: . ABETA- BBETA I FORTRAN FOR.~T:

Read from Subroutine:

(14ES.O)

MODEL 1*

Format* Description I

Variable Columns CG I

ABETA 1-5 ES.O The.mixing parameter Bis defined as 10 -

SaABETA*(RE**BBETA} where REsReynolds I

.BBETA 6-10 ES.O 1 Number 10 I

Notes:

(1) If NlaO, ABETA, BBETA ar~ set to a.oz and 0.0 respectively.

I (2)- Thermal Conduction between channels is suppTessed for all Nl.

I I

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• 1 I

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I.

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I -241-I Card(s) Type TlO Single Phase Friction ~.~odel Required.to be present Only if NZ (on T8) "> 0 I FORTRAN READ list:

• NVISCW, (A(J), B(J), C(J), J=l, 4)

FORTR.t'\N FOR..'1l'i.T: (15, 13ES.O)

Read. from Subroutine: MODEL I

Variable Format*

I Columns Description CG NVISCW 1-5 IS .=l, if the wall viscosity correction 2 I to the single phase friction factor is required. '

=O, if not required.

I *A 6-65 ES.O The single phase friction factor is 2 I B c

6-65 6-65 ES.O ES.O

} calculated as A*(RE**B)+C, where RE=Reynolds Number.

I Notes:

I (1) The.jriction factor defined by A(J), B(J),C(J) is applied to those channels with that value of J on card T2. If all chan-nels have the same friction factor, J is given a5 1 on carJ T2 fot all channel types and only A(l), B(l), C(l} ~iven on card TIO.

I (2) If NZ=O, NVISC is set to 0 and the smooth tube friction factor is used, i.e., A:0.184, B= -0.2 and C=O.O for a11 J=l,4.

I '

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t I

-242-I Card(s) Type Tll Two Phase Friction Model I

Required.to be .present Only if N3 (on TS)>O I

FORTRAi.~ READ list: J4 FORTR.t"\N FORJ.'1.AT: (1415) I MODEL Read. !rom Subroutine:

I Variable Columns Forruat* Description CG I J4 1-5 IS Two phase friction correlation trigger J4=0 Homogeneous Theory

=1 Armand

=2 Baroczy

=3,4 ,Not in use

=s Polynomial in quality I

Note: I If N3=0, J4 is *set to O.

I I

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I

'i

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I

I -243-I Card(s) Type Tl2 Required.to *be present FORTRA.i.~ READ list:

• Two phase friction polynomial Only if J4 (on Tll)

NF

=

(AF(L), L=l, NF)

S I FORTRAN FOPMAT: (!S, 13ES.O)

Read. from Subroutine: MODEL I

Variable I Columns Format* Description CG NF 1-5 IS No. of terms in polynomial (max=7) 2 I AF 6-40 ES.O Polynomial coefficients 2

'I Notes:

I (1) The two phase friction multipli.er*is calculated as I  ;'=NF*

~. (AF(-t-)f*l)

I whe.re 1*

x = quality co~x<:1)

I I '

I I

I I

j I

.. -------*-*r-

-244-Card(s) Type Tl3 Void Fraction Model I

.. ,.,' Required.to be present FORTRlu~ READ list:

Only if N4 (on TS)> 0 JZ J3 I

FORTRAN FOR..~T: (14IS) I Read. from Subroutine: MODEL I

Variable Columns Format Description CG I J2 1-5 .IS Subcooled Void Indicator 2 I

J3 6-10 IS Slip Ratio Indicator z ,,

JZ=O no subcooled void

• =1 Levy subcooled void correlation I

J3=0

=l

=2

=3,4 Slip Ratio=l Armand Slip Ratio Correlation Smith Slip Ratio Correlation Not in use.

=S Slip ratio given (T14)

=6 Void fraction as a polynomial in quality (Tl4) I Note: I If N4=0, JZ and J3 are both set to 0.

\

I I

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I

) I I

I -245-I Card(s) Type Tl4 Slip Ratio l i

Required.to be present Only if J3(on Tl3)=5 or 6 I FORTRAJ.'l READ list: NV (AV(L), L=l, NV)

I FORTRAN FORMAT:

Read. from Subroutine:

(IS, 13ES.0)

MODEL I

Variable Columns Format' Description CG I

NV 1-5 IS No.* of terms in polynomial (~7) 2 I AV 6-40

• ES.O Polynomial coefficients 2 I

I A polynomial ty (O~X~l).

r.. *

,.I: tN (AY (dX) is calculated ~here X=quali-I For J3= 5, NV should be se.t to 1 and only one val:';.le in. The slip ratio is taken as AV(l).

of AV read For J3=6~ up to 7 values of AV may be read in a.n.d the void frac-I tion is calculated as a polynomial in X, namely:

~ NV (A Y- (y-) x,.__,)

I "r=l I

I I

I 1*

i I

-246-I Card{s) Type TIS Inlet Flow Model I Required.to be present* Only if NS (on TS)> 0 FORTRA.i.~ READ lis.t: IG I FORTRAN FOR:*lAT:

Read. from Subroutine:

(14IS)

MODEL I

I Variable Columns Format Descriot:ion CG I

IG 1-S IS Inlet Flow Indicator 11 I

IG =0 IG. = 1

• Inlet mass velocity* same for all channels Inlet mass velocities for channels calculated to I

give same inlet pressure gradient IG =2 Inlet mass velocities gi~en (on Tl6) I Note I (1) If NS

• O, IG set to O.

I I

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I

)

I I

1* 247-1 Card(s) Type Tl 6 Inlet Flow Distribution

• Required'to be present Only if IG (on TlS) = Z I FORTRAN READ list: * (GR(I), I=l, NCHANL)

I FORTRA.i.'l FOR....,1AT: (i4ES.O)

Read. from Subroutine: READ IN/MODEL

-1

-I Variable Colurins Format Description CG GR 1-70 ES.O Inlet Mass Velocity Ratio (local/ 11 I average) for all NCHA.~L channels I

I I

I I

I '

I I

I I *.

I I

I -248-Card(s) Type:

I Required to be present:

Tl7 Parameters Only i f N6>0 I- FORTRAN READ list: KIJ FTM SL THETA FORTRAN FORMAT: 14E5.0 I Read from Subroutine: MODEL I Variable Columns

- -- Format Description KIJ 1-5 E5.0 Crossf low resistance coefficient, k I FTM 6-10 E5.0 Turbulent momentum fac1:or', Ft I SL THETA 11-15 16-20 E5.0 ES.O Transverse momentum factor, s/'J..

Inclination of channel to vertical (d~grees)

I I

I NOTE:

If N6 = O; KIJ set equal to 0.5, FTM to 0.0, SL to 0.5, and THETA to 0.0 (i.e.,

1. vertical).

I I

I I

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I I.

I -249-I Card(s) Type Tl8 Convergence Criteria Required.to be present* Only if Ni (on TS)> 0 I FORTRAN READ list: NTRIES FERROR 1* FORTRAN FORMAT: (IS, 13 ES.O)

Read. from Subroutine: MODEL I

Variable. Col um.Tis Format I Description CG NT RIES 1-5 IS Maximum permis*s z.b le number of hy- 9 I draulic iterations FERROR 6-10* ES.O Flow convergence criterion 9 I Note I (1) If N7=0, NTRIES set to 20 and FERROR to 0.001.

I I

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i I

-250-I card(s) Type Required.to be Tl9 present Physical Properties Only if NS (on TS)) 0 I

FORTRAi.~ READ list: NPROP N PH P2 I FORTRAN FORMAT: (215, 2ES.O)

Read. from Subroutine: MODEL I Variable Columns Format* Description CG I

NPROP 1-5 ES.O No. of pressure points in physical 1 I

property table for interpolating IS between (Minimum=2, Maximurn=30).

a*l or 2 (see PH below)

I N 6-10 PH 11-15 ES.O N=l, PH=lowest pressure (psia) in problem.

I N=2, PH=lowest enthalpy (Btu/ib) in problem, from which the lowest pres-sure is calculated (see below).

I P2 16-20 ES.O Highest pressure in problem.

I Notes I

(1) From this card, a table containing NPROP equi-spaced values of pressure from Pl (see below) to P2 is constructed g*iving relevant physical properties- -calculated from polynomial expressions - - at.

I each pressure. Physical properties at intermediate pressures are

found by linear ~nterpolation. I (2) It is important that the table spans the physical property range of the problem. For example, with inlet subcoolir.g, the inlet en-*

enthalpy would correspond to a pressure lower than the reference value; I

the pressure would be that at which the enthalpy was the saturation value. Hence the first pressure in the table should be lower than the value correspo~ding to the lowest steady state or transient I

enthalpy .encountered, so that the other physical properties at that enthalpy may be properly interpolated. If N*l, PH is given as Pl1 the lowest pressure in the problem and if N=Z, as the lowest enthal-I py--the lowest pressure Pl is then calculated from PH.

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-(3) puter.

If N8=0, NPROP"is set to 30 and Pl, PZ calculated by the com-I I

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I -251-I I Card(s) Type Tl9a Coupling parameters Required to be present Only if N9 (on TS) O I FORTRAN READ list:

(ENEH(K), K=l,NK) where NK=total number of boundaries I FORTRAN FORMAT: 14E5.0 I Read from Subroutine: MODEL I Variable Columns Format Description ENEH 1-70 E5.0 Coupling parameter introduce in the mixing I term of the energy conservation equation.

I I Note: The order in which these coupling parameters should be entered I is the same as the one described in card T6a for interconnection between channels.

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-252- I Card(s) Type T20 Steady State Operating C-0nditions I Required.to be present Alliays FORTRAN READ list:

• IH HIN GIN PEXIT I

FORTRAN FORMAT: (IS, 13ES.O I Read. from Subroutine: OPERA I

Variable Columns Format Description CG I

IH 1-5 IS Inlet Enthalpy Indicator 11 HIN 6-10 *Es.a IH=O: Inlet Enthalpy (Btu/lb) ~ ~

.1..1.

I IH=l:

IH=2,3:

Inlet Temperature (°F)

HIN not used, set to zero I

(see T21}.

GIN 11-15 ES. 0 Average 2 Inlet Mass Velocity 11 I

.(Mlb/ f):. hY)

PEXIT 16-20 ES.O System pressure (psia) 11 I I

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I -253- ....... -; -

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Card(s) Type T21 Inlet Enthalpy Distribution

• -" Required.to be present Only if III =2 or 3 I FORTRAN READ list: (A(I), I=l, NCIIANL)

I FORTRAN FORMAT:

Read from Subroutine:

(i4ES.O)

READ IN/OPERA I

Variable Columns Format Description CG I A 1-70 ES.O IH=2: Inlet enthalnies for each 11 I IH=3:

channel (Btuilb)

Inlet temneratures for each channel (° F)

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-254- I Card(s) Type T2Z Transient Indicators I Required.to be present FORTRAi.~ READ list:

Always NP NH NG NQ I

FORTRAN FOR.i.'1A':': (14! 5) 1.-

Read. from Subrnutine: OPERA I

Variable NP Columns 1-5 Format*

IS Descri?ticn No. of points at which pressure tran-CG 11 I

sient forcing function will be given (T23). Maximum=30 I NH 6-10 IS As NP but inlet enthalpy (TZ 4) . Ma- 11 ximum=30 I

NG 11-15 IS As NP but inlet flow (TZ 5) . Maxi- 11 NQ 16-20* IS mum=30 As NP but channel power (T2 Sa) . 11 I

Maximum=30 I

Notes (1) NQ is only given in COBRA but not in MEKIN (leave NQ blank) I as In MEKIN, the transient channel power is obtained from the Neu-

.tronics.

(2) If only steady state calculations are required, T22 may be a I

blank card.

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I -255-I Card(s) Type T23 Pressure Transient Forcing Function Required.to be present Only if NP)l (T22)

I FORT.RAN READ list: (YP (I) , FP (I) , I= 1 , NP)

I FORTRAN FORi.'-lAT: (14ES. 0)

Read. from Subroutine: READ IN/OPERA I

Variable Columns Format*

I Description CG yp 1-70 ES. 0

• Time (seconds) 11 I FP 1-70 ES.O Ratio of transient to steady stat~ 11 pressure at time YP I

Notes I (1) YP(l), FP(l) should be given as 0.0 and 1.0 respectively.

I (2) The value of FP at a time intermediate between two values of YP is found by linear interpolation.

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-256- I card(s) Type T24 Inlet Enthalpy Transient Forcing Function I Required.to be present FORTRAN READ list:

• Only if NH>l (T22)

(YH(I), FH(I), I=l, NH)

I FORTR.1\N FOR..'1AT: (14ES.O) I Read. from Subroutine: READ IN/OPERA I

Variable YH Columns 1-70 Format ES.O Description Time (seconds)

CG 11 I

FH 1-70 ES.O Ratio of transient .to steady state 11 I

enthalpy or temperature (depending on IH--card T20) at time Y.H. I Notes I (1) As for card*T23~ but YH, FH instead of YP, FP.

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I -257-I card(s) Type T25 Required.to be present*

Inlet Flow Transient Forcing Function Only if NG> 1 (T22)

I FORTRAN READ list: (YG(I), FG(I), I=l, NG)

FORTRAN FOTh"1AT: (14ES. O)

I Read. from Subroutine: READ IN/OPERA I

Variable Columns Format Description CG I YG 1-70 ES. 0

• Time (seconds) 11 I FG 1-70. ES.O Ratio of transient to steady state 11 average mass velocity at time YG I

Notes I (1) As for card T23, but YG, FG instead of YP, FP.

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- 2 5 8---:_-- - --- --::-.:-

I Card(s) Type T25a Inlet Power Transient Forcing Function I Required-to be present*

FORTRAN READ list:

Only if NQ > 1 (T22) and IQP3=2 (CS)

(YQ (I) , FQ (I) , I=l, NQ)

I FORTRAN FORMAT: (14ES. 0) I Read. from Subroutine: READ IN/OPERA I

Variable Columns Fonnat

---

Description CG I YQ 1-70 ES.O Time (seconds) 11 I FQ 1-10* ES.O Ratio of transient -::o steady state 11 channel power at time YQ I

Notes (1) As for card T23, but YP, FQ instead of YP, FP.

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I -259-I Card ( s) Type T26 "Debug" Option Required.to be present Always I FORTRAN READ list: KDE BUG I FORTRA.i.'1 FORM.Z\T:

Read from Subroutine:

(1415)

TABLES I

Variable Columns Format* Description CG I 9 KDE BUG 1-5 IS '.'Debug" option I =O: normal--no tes~ printing

=l: "debug"--with 1test printing I

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-260-I card(s) Type T27 Output Printing I Required.to be present Always FORTRAJ.'1 READ list: NSKIPX NSKIPT NOUT NPCHAN NPROD I

NPNODE FORTRAN FORMAT: (14IS)

I Read from Subroutine: TABLES I

Variable NSK I PX Columns 1-5 Format I*S Description Axial print option CG 9

I

=O or 1: every axial step printed

)1 each (NSKIPX)th step pri~ted I

NSKIPT 6-10 IS Time step option 9 As for NSKIPX but time (not axial) steps I NOUT 11-15 IS =O:

=l:

print channel results only channel + cross flow tables 12 I

=2: channel + fuel temperature tables

~3: channel + cross flow + fuel temperature tables I NP CHAN 16-20 *rs =O: all channels printe<l 12

'l: read in NPCHAN channels to be printed I NP ROD 21-25 IS As for NPCHAN but rods instead of 12 channels I NPNODE 26-30 IS As for NPCHAN but radial fuel nodes 12 instead of channels I

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I -261-I card(s) Type T28 Channels to be printed Required.to be present Only if NPCHAN (T27) .S 1 I FORTfu"\N READ list: * (PRINTC(I), I=l, NPCHAN)

I FORTRAN FOill-l~"\T:

Read. from Subroutine:

(1415)

TABLES I

Variable Columns Format* Description CG I

IS Identification Number of channels ~o 12 I PI.UNTC 1-70 be printed.

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-262-I Card(s) Type T29 Rods to be printed I Required.to.be present FORTRlili READ list:

Only if NPROD (T27) ~ 1 (PRINTR(I), I=l, NPROD)

I FORTRAN FORMAT: (14IS) I Read from Subroutine: TABLES I

Variable Column3 Format Descrioticn CG I

PRINTR 1-70 IS Identification Number of rods to 12 be .printed. I I

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,. -263-

'I card(s) Type T30 Fuel nodes to be printed Required.to be present Only if NPNODE (T27) ~ 1 FORTR.Ai.'1 READ list: (PRINTN(I), I=l, NPNODE)

I FORTRAN FORi."1AT:

Read ..from Subroutine:

(1415)

TABLES I

Variable Columns Format Description CG I 12 PR I NTN 1-70 IS Radial fuel nodes ~o be printed I l=rod center, (NOTIESF + l)=outer clad surf ace I

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-264-I Card(s) Type C4 End Input Data, start calculation I Required.to be present FORTRAi.~ READ list:

Always BLANK CARD I

FORT&\N FORMAT: I Read from Subroutine: INDAT I

Variable Columns Format Description CG I

c 0

N T

I Note: R At this point in the calculation, control returns to reading 0

L I

Card C4. If NGROUP 2 1-12, more Input Data are read in the original COBRA format, these** later data overwriti*ng what has already 'been read in. If NGROUP = O, calculation starts. I I

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1* -265-I Card(s) Type C12 Nodal Power ~!ul tiplier 1* Required.to be present Only if IQP3 (CS) = 1 ar 2.

FORTRAN READ list: ZM I FORTRAN FORMAT: (8E10.0)

Read. from Subroutine: QPR3 I

I Variable Columns Foor.at Description CG ZM 1-10 ElO .*O Nodal Power Multiplier I

I ZM= -2.0:

ZM= -1~0:

Reset to 1000.0/3.6 Reset to 3413.0/3.6 (MBtu/h~ to Btu/s)

(MW to Btu/ s)

I ZM >' 0. 0: ZM unchanged 1* The nodal powers given on cards Cl3, Cl4 are all m.ml tip lied by ZM.

This allows, for example, units to be converted.

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-266-

-1 Card(s) Type Cl3 Fuel Nodal Powers I*

_,- Required.to be present FORTRAi.~ READ list!

• Only if IQP3 (C8) =1 or 2

((QF(I,J), J=l, NDX), I=l, NCHANL)

I FORTRAN FORMAT: (8El0.0) I Read_ from Subroutine: QPR3 I

Variable Colum..""ls Format _Descriotion CG I

Average Fuel Nodal Power for Chan-QF 1-80 8El0~0 nel I, axial interval J to (J+l) I The power for each channel I (I=l, NCHANL) is read in turn. Each channel-set, i.e., J=l,*NDX, starts on a new card, continuing onto I the next card if NDX > 8. The uni ts of QF in the calculation. are Btu/sec. They may be read in those units (when ZM=l.O on Cl2) or converted using ZM. NDX is read on card cii.-* I I

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I -267-I Card(s) Type Cl4 Coolant Nodal Powers Required.to be present Only if IQP3 (CS) = 2 I FORTRAN READ list: * ((QC(I,J), J=l, NDX), I=l, NCHANL)

FORTRl\N FORMAT: (8El0.0)

I Read. from Subroutine: QPR3 I

Variable Columns Format Description CG I QC(I,J) 1-80 8El0~0 Average Nodal Power deposited in Coolant for channel I, axial inter,val I J to J+l.

I As for card Cl3, but QC instead of QF.

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-268- I I

l Card(s) Type Cl3 Transient Fuel Nodal Po11J.er

)

~-

Required.to be present Only if IQP3 = 1 or 2 and NDT> 1 FORTRAN READ lis.t: ((QF(I,J), J=l, NDX), I=l, NCHANL) I FORTRAN FORMAT:

Read. from Subroutine:

(8El0.0)

QPR3 I

Variable Columns Format*

I Description CG I

Cards Cl3 and (if IQP3=2) Cl4 are read for the first transient time step, then both sets of cards for the next time step, etc.

until data for* all time steps have been given.

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1- . ---*-----*-****-*-**.

,. -269-Card(s) Type Required.to be present FORTRAi.~ READ list:

Cl4 Transient Coolant Nodal Power Only if IQP3= 2 and NDT) 1

((QC(I,J), J*l, NDX)~ I=l, NCHANL) 1* FORTRAN FORMAT: (8E10.0)

Read. from Subroutine: QPR3 I

I Variable Columns Format* Description CG

1. See last card, "transient" Cl3.

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-27f}-

I Card(s) Tvoe C3 Required.to be presen~ Always I

FORTRAN READ list:

FORTRA.."I FORM}i..T:

IP ILE. KASE Jl TEXT I

(Il, I4, IS, 17A4)

Read from Subroutine: INDAT I Variable Columns Format Description CG I

See earlier C3

• I Note I

• At the end of the calculation, control returns again to the read

. statement for card C3.

I If KASE> 0; the next case is read.

If KASE =O (e.g., a blank card), calculation stops.

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NOTICE -

THE ATTACHED FILES ARE OFFICIAL RECORDS OF THE DIVISION OF DOCUMENT CONTROL. THEY HAVE BEEN CHARGED TO YOU FOR A* LIMITED TIME PERIOD AND MUST BE. RETURN.ED TO THE RECORDS FACILITY BRANCH 016. PLEASE DO NOT SEND DOCUMENTS CHARGED OUT THROUGH THE MAIL. REMOVAL OF ANY PAGE(S). FROM DOCUMENT FOR REPRODUCTION MUST BE REFERRED TO FILE PERSD~~~ z:t)'.2.2i \ .

DEADLINE RETURN DATE ~33g tiY l lJ r\8-t-C\

RETURN m* REACTOR D.~~KET FltES ~-

!fq l02l\- o5q,LL * , .*

' REcdRDS FACILITY.BRANCH