Atomic Energy of Limited

CALCULATION OF FAST FLUX

IN REACTOR PRESSURE TUBES AND EXPERIMENTAL FACILITIES

by

P.C. BARNETT

Chalk River, Ontario

July 1968

AECL-3167 A E C L-31 6 7

Calcul d.es flux neutroniques rapides dans les tubes de pression et dans les liistalTaiions experimentales des rgacteurs par P.C. Barnett (CGE)

Resume - Le programme de calculatrice EPITHET a servis a calculer les flux neutroniques rapides (>1 MeV) dans plusieurs tubes de pression et installations expgrimentales de reacteurs dans le but de comparer ces flux dans diffgrents cas et d'obtenir un ensemble harmonieux de valeurs de flux pouvant etre employe pour etablir un rapport entre les contraintes de fluage et les flux neutroniques rapides. Les installations prises en consideration sont indiquees ci-dessous ainsi que les flux calculus de rapides (>1 MeV).

Flux rapide n n13 t 2 10 n /em s NPD 1.14 Douglas Point 2.66 Pickering 2.89 Gentilly 2.35 SGHWR 2.65 NRU U-1 & U-2 Tube de pression 3.25" - Combustible a 19 Elements 3.05 NRU U-1 & U02 Tube de pression 4.07" - Combustible k 28 elements 3.18 NRU U-1 & U-2 Tube de pression 4.07" - Combustible a 18 elements 2.90 NRX X - 5 0.88 PRTR Combustible Mk I 2. 81 PRTR Combustible HPD 3. 52 WR-1 2.73 Machine de fluage Mk IV (NRX) 0.85 Machine de fluage Mk VI (NRU) 2. 04 Echantillon biaxial de fluage inserg (NRU U-49) 2.61

Chalk River, Ontario Juillet 1968 CALCULATION OF FAST NEUTRON FLUX IN REACTOR

PRESSURE TUBES AND EXPERIMENTAL FACILITIES

by

P.C. Barnett*

S Y N O P S I, S

The computer program EPITHET was used to calculate the fast neutron flux (>1 MeV) in several reactor pressure tubes and experimental facilities in order to compare the fast neutron flux in the different cases and to provide a self-consistent set of flux values which may be used to relate creep strain to fast neutron flux. The facilities considered are shown below together with the calculated fast neutron flux (>1 MeV) .

Fast Flux 10-*-3 n/cm^s

NPD 1.14 Douglas Point 2.66 Pickering 2 .89 Gentilly 2 .35 SGHWR 3 .65 NRU U-l and U-2 3.25" Pressure Tube - 19 Element Fuel 3 .05 NRU U-l and U-2 4.07" Pressure Tube - 28 Element Fuel 3 .18 NRU U-l and U-2 4.07" Pressure Tube - 18 Element Fuel 2 .90 NRX X-5 0.88 PRTR Mk I Fuel 2.81 PRTR HPD Fuel 3 .52 WR-1 2 .73 Mk IV Creep Machine (NRX) 0.85 Mk VI Creep Machine (NRU) 2 .04 Biaxial Creep Insert (NRU U-49) 2.61

Chalk River, Ontario July 1968

AECL-3167

* Attached Staff, Canadian General Electric. CALCULATION OF FAST NEUTRON FLUX IN REACTOR

PRESSURE TUBES AND EXPERIMENTAL FACILITIES

by

P.C. Barnett*

1.0 INTRODUCTION

The in-reactor creep of pressure tubes is being evaluated by several methods in different reactors. In order to relate the creep strain to fast neutron flux (>1 MeV) ( and to compare the results from different experiments, the fast neutron flux in each facility must be calculated by the same method. The prediction of pressure tube behaviour in power reactor service is also dependent on a consistent method of flux; calculation which will relate the experimental conditions to the power reactor operating conditions. The computer program EPITHET(2)(14)was therefore used to calculate the fast neutron flux (>1 MeV) in the pressure tubes and test specimens in the following facilities:

NPD ( Demonstration) Douglas Point Pickering Gentilly SGHWR (Steam Generating Moderated Reactor) NRU U-l and U-2 3.25" Pressure Tube - 19 Element Fuel NRU U-l and U-24.07" Pressure Tube - 28 Element Fuel NRU U-l and U-2 4.07" Pressure Tube - 18 Element Fuel NRX X-5 PRTR ( Recycle Test Reactor) WR-1 (Whiteshell Reactor-1) Mk IV Creep Machine (NRX) MkVI Creep Machine (NRU) Biaxial Creep Insert (NRU U-49).

The effects on fast flux of boiling, the power of surrounding sites, and fuel enrichment are also reported. The

^Attached Staff, Canadian General Electric. _ 2 -

effect of neutron energy level is being studied and will be the subject of a separate report.

2.0 METHOD OF CALCULATION

The computer program EPITHET uses the methods of multi­ group multi-region collision probability theory to calculate the flux spectrum in any region of the lattice cell. The particular geometry under consideration is divided into 30 annular regions and the fuel is therefore homogenized as shown in Pig. 1. The model uses the same amount of each material as the actual fuel and the fuel rings are located at the same radius as the actual fuel. The flux is calculated for each energy group and is then integrated above 1 MeV, giving the fast neutron flux in each region. The cross-section data and an example of the geometry data input is given in Appendix 1.

The fast flux calculated by EPITHET was normalized to a fuel power of 1 kw/cm (Appendix 1). The fast flux in any facility was therefore obtained by multiplying the flux factor (K) from EPITHET by the fuel power (P) in kw/cm.

3.0 POWER REACTORS

3.1 General

Information concerning NPD^^ , Douglas Point Pickering^, Gentilly(^) and S.GHWr (^) is shown in Table 1 and the dimensions of each fuel channel are shown in Figs. 2-5.

3.2 Fast Neutron Flux

The fast neutron flux (>1 MeV) in the pressure tubes of each reactor is shown in Table 2. The flux is calculated at the maximum flux position (i.e., at the midpoint of the central fuel channel in each reactor) using the nominal maximum fuel linear power rating (P). The relationship between J'kdB and P is shown in Appendix 2.

4.0 EXPERIMENTAL FACILITIES

4.1 NRU U-1 and U-2 Lo o p s

4.1.1 General

The NRU U-1 and U-2 loops are installed in the NRU reactor - 3 -

and are used to irradiate reactor fuel and pressure tubes under conditions similar to those expected in power reactor service. The loop configuration using a 4.07" pressure tube with a 28 element fuel bundle is shown in Fig. 6. The 3.25" pressure tube case is similar, but has a 4.425" calandria tube with 0.172" wall.

4.1.2 Coolant Boiling

In order to determine the effect of coolant boiling on fast neutron flux, the flux in the NRU U-l and U-2 loops was calculated for several values of coolant density. These results are shown in Pigs. 1, 8 and 9 for each of the geometries considered.

The graphs show that the flux factor K (and therefore the fast neutron flux at the pressure tube) increases as the coolant density decreases. The coolant absorbs and scatters fewer neutrons as its density decreases thereby permitting more fast neutrons to reach the pressure tube.

The steam quality at the normal operating pressure for each fuel type is shown for reference on each of the graphs. A steam quality of 10% increases the fast neutron flux at the pressure tube by about 10% from the value with saturated water coolant.

4.1.3 Power of Surrounding Rods

The standard NRU fuel rods are 1.732" in diameter and consist of 12 fuel elements. Each element has a 0.216" diameter enriched -aluminum alloy core clad in a finned aluminum sheath. These fuel rods have a much lower power than the fuels tested in the loops (eg•, 800 kw for the NRU fuel compared with 2000 kw for a 3.25" loop fuel) .

The computer calculations were made using two cell boundary conditions:

(i) assuming neutron incurrent = neutron outcurrent, i.e., adj acent rods are identical

(ii) assuming neutron incurrent = 0, i.e., adjacent rods have zero power.

During a normal operating period in NRU the power output of the sites surrounding a loop lies between the two extreme conditions of (i) and (ii). An interpolation is therefore made to allow for the - 4 -

actual power of the surrounding sites and an example of the inter­ polation procedure is given below.

Example

Power outputs during a 1200 hour period of operation of the U-103 ph II experiment were 2000 kw for the loop and a total of 3135 kW for the 6 surrounding sites.

Interpolation for the 3.25" pressure tube case using a coolant density of 0.75 gm/cc and values of K from Fig. 7 give the flux factor as follows:

K = 2.93 x 1012 +r7r-— x (3 .35 - 2 .93)1 x 1012 l_6 x 2000 J

12 2 = 3.04 x 10 n/cm s per kw/cm.

Similar calculations were made for the other loop geometries and the results are shown in Appendix 3 and plotted in Figs. 7, 8 and 9 .

The graphs show that there is a difference of approximately 15% between the 'adjacent rods identical' and 'adjacent rods zero' cases. The 'adjacent rods zero' condition is much closer to the actual operating condition (curve obtained by interpolation), the difference between the two cases being about 4% for 19 element fuel, 3% for 28 element fuel and 1-1/2% for 18 element fuel. Thus when the fast neutron flux is calculated using the 'adjacent rods zero' condition, the surrounding rods have only a small effect, particularly in the 4.07" pressure tube cases.

4.1.4 Examples of Fast Neutron Flux in U-l and U-2 Pressure Tubes

Examples of the fast neutron flux at the midpoint of pres­ sure tubes in the U-l and U-2 loops are shown in Table 2. The examples are taken from the same operating periods that were used to plot the interpolation curves and these periods are listed in Appendix 3.

The fast neutron flux is directly proportional to the fuel power, so that the trend towards increasing the fuel power in loop experiments will result in correspondingly higher fast neutron fluxes in the pressure tubes. - 5 -

4.1.5 Fuel Enrichment

The value of the flux factor K was determined for several fuel enrichments using data from the 28 element fuel bundles of the U-209 fuel experiment and a coolant density of 0.75 gm/cc. The results shown in Table 3 indicate that fuel enrichment has little effect on the value of the flux factor K. The power output of an enriched uranium fuel bundle is higher than that of a natural uranium bundle, however, so the fast neutron flux in a pressure tube adjacent to an enriched bundle is correspondingly higher.

4•2 NRX X-5 Loop (9) The X-5 loop occupies the central position in the NRX reactor and has a 3.25" pressure tube surrounded by a cooling jacket as shown in Fig. 10. The loop is used for many different experimental fuels and the fast neutron flux at the pressure tube depends on the par­ ticular fuel experiment. The fast flux should therefore be cal­ culated for each fuel experiment during the life of the pressure tube in order to obtain the accumulated dose. An example of the fast flux is shown in Table 2 using operating data from the X-522 fuel experiment.

4.3 PRTR

The cross-section of a PRTR fuel channel is similar to NPD (Fig. 2). The fast neutron flux in PRTR was calculated for two types of fuel. The Mk I fuel is a 19 element natural UC>2 fuel bundle(10) and was used in the core prior to the recent uprating to High Power Density (HPD) fuel. The HPD fuel is a 19 element fuel bundle using UC>2 - 2% PuC>2 (H) . The fast neutron flux in the pres­ sure tube is shown in Table 2 and is calculated at the midpoint of the central channel using the nominal maximum linear power rating of the fuel.

4.4 WR-1 ( 12) The cross-section of a WR-1 fuel channel with a stain­ less steel pressure tube is shown in Fig. 11. The fast neutron flux in the pressure tube is shown in Table 2 and is calculated at the midpoint of the central channel using the nominal maximum linear power rating of the fuel. Zircaloy-4 pressure tubes installed in the reactor would experience a slightly lower fast neutron flux than the stainless steel pressure tubes as shown in Table 2. Zircaloy-4 has a slightly higher absorption and scattering cross-section in the 1 MeV to 10 MeV range than stainless steel and the Zircaloy-4 _ 6 -

pressure tube has a 0.075" wall compared with 0.040" for the stain­ less steel pressure tube. Both these factors would lower the fast neutron flux in the Zircaloy-4 case.

4.5 Fast Neutron Facilities in NRX and NRU

4.5.1 General

The power of a fast neutron rod is normally quoted in terms of the total power output (MW) rather than as a maximum linear power (kw/cm). The fast neutron fluxes reported in this section are there­ fore quoted for a fuel rod power of 1 MW and for any other power the flux is multiplied by the rod power in MW.

4.5.2 Creep Machines

The fast neutron flux (>1 MeV) for the test specimens in the NRX Mk IV and the NRU Mk VI creep machines (^ ) is shown in Table 4. The fast flux is shown for a rod power of 1 MW and also for typical operation of each fast neutron rod. The effect of the surrounding sites has been taken into account and a sample calculation for the creep test Ru-5 is shown in Appendix 4. Flux factors for the NRX creep machine are also given in Appendix 4.

The neutron absorption and scattering by the components of the creep machines have been taken into account in the results shown in Table 4. The magnitude of the absorption is calculated by com­ paring the flux at the centre of an empty fast neutron rod with the flux when the creep machine is inserted. The Mk IV creep machine reduces the fast flux by 1% and the Mk VI machine reduces the fast flux by 19%. The water jacket and cooling coils on the Mk VI machine account for the extra absorption.

4.5.3 Biaxial Creep Insert (NRU U-49)

The Biaxial Creep Insert shown in Fig. 12 consists of 0.9" diameter pressure tube specimens which are placed inside an NRU fast neutron rod. The specimens are machined to different wall thicknesses to provide hoop stresses ranging from 15,000 to 39,000 psi. The specimens are positioned to provide creep information in fast flux, thermal flux and out-of-flux regions.

The average fast neutron flux >1 MeV in the specimens in the fast flux region of the experiment is shown in Table 4 for a rod power of 1 MW. An example using the rod power during the first -7-

operating period is also shown in Table 4 and the calculation is shown in Appendix 5.

5.0 CONCLUSIONS

1. The calculation of fast neutron flux >1 MeV for various experimental facilities and power reactors using the computer program EPITHET provides a self-consistent set of flux values which may be used to relate experimental results with each other and with conditions expected in reactor service.

2„ Coolant boiling has an effect on fast neutron flux and should be taken into account when evaluating the results of loop experiments.

3. The power of adjacent rods has an effect on fast neutron flux and should be taken into account when evaluating the results of loop experiments. An approximation of the fast flux may be obtained using the 'adjacent rods zero' condition.

6.0 ACKNOWLEDGEMENTS

The author wishes to thank M.J. Halsall and P. Garvey for advice on the use of EPITHET and R.B. Lyon for supplying the program and cross-section data. Helpful discussions with P.A. Ross-Ross and advice from E. Critoph are gratefully acknowledged.

7.0 REFERENCES; .

1 . P.A. Ross-Ross and C.E.L. Hunt, "The In-Reactor Creep of Cold-Worked Zircaloy-2 and Zirconium-2.5 Wt % Niobium Pres­ sure Tubes", J. Nuol. Mater. 26: 2-17 (19 68).

F.E. Driggers, "AUiMethod of Calculating Neutron Absorptions and Flux Spectra at Epithermal Energies", Atomic Energy of Canada Limited publication AECL-1996 (1964).

"The Engineering Design and Operation of the NPD Reactor" Atomic Energy of Canada Limited publication AECL-1682 (1963). Papers summarized in Trans. Amer, Nuol Soo. 5: 445-451 (1962).

J.N. Fairlie, "Douglas Point Nuclear Generating Station", Atomic Energy of Canada Limited publication AECL-1596 (1962).

C.E. Beynon, "The Pickering Nuclear Generating Station", Atomic Energy of Canada Limited publication AECL-2214 (1965), Canadian Nuclear Association paper 65-CNA-204 (1965). - 8 -

6. G .A . Pon, "CANDU-BLW Progress Report", Atomic Energy of Canada Limited publication AECL-2554 (1966); Canadian Nuclear Association paper 66-CNA-302 (1966).

7. A. Firth and J.E.R. Holmes, "The SGHWR Prototype Reactor" Nucl. Eng. 9: 46-49 (1964).

8 . M.D. Ferrier (editor), "The NRU Reactor - Lectures Given at Chalk River, Ontario, Feb-April 19 56, Atomic Energy of Canada Limited publication AECL-507 (1957).

9. R.E. Manson and H.E. Smyth, "The NRX Reactor - A General Description", Atomic Energy of Canada Limited publication AECL-269 2 (1967).

10. N.G. Wittenbrock, P.C. Walkup and J.K. Anderson (editors) "Plutonium Recycle Test Reactor Final Safeguards Analysis," General Electric Co., Hanford Atomic Products Operation publication HW-61236 (19 59).

11. J.R. Worden, et al,"Physics Experiment: High Power Density Core of the PRTR, "Battelle Memorial Institute, Pacific Northwest Laboratory publication BNWL-221 (1966).

12. "WR/1 Whiteshell Reactor No. 1" Can. Nuol. Teoh. 4: (4) 30-34 (1965); Reprint AECL-2367.

13. V. Fidleris, et. alIn-Reactor Creep Machines", Atomic Energy of Canada Limited publication AECL-2568 (1966).

14. M.J. Halsall, "Modifications to the Computer Code EPITHET," Atomic Energy of Canada Limited publication AECL-1996 (supplement) (1966).

15. J.A.L. Robertson, "/kd0 in Fuel Irradiations", Atomic Energy of Canada Limited publication AECL-807 (1959). - 9 -

Table 1

Power Reactor Data

Reactor Power MW(e) No. of Channels Coolant Fuel . channel Cross-Section

NPD 20 132 Fig. 2 D2° Douglas Point 200 306 Fig. 2 D2° Pickering 500 390 D2° Fig. 3 Gentilly 250 308 H2° Fig. 4 SGHWR 100 112 Fig. 5 H 2° Table 2

Fast Neutron Flux in Reactor pressure Tubes

Reactor Pressure Tube Flux Factor Jkae Bundle Linear Fast Flux and Fuel Description from EPITHET w/ cm Power (>1 MeV) K P kw/cm jz£ = KxP n/cm2 s per kw/cm n/cm2s 13 NPD 2.91 x 10 18 3 .91 1.14 x 10 12 Douglas Point 3.05 x 10 40 8.71 2.66 x 1013 12 Pickering 2.18 x 10 41.8 13.25 2.89 x 1013 12 Gentilly 2.35 x 10 48 10.0 2.3 5 x 1013 12 13 SGHWR 1.66 x 10 48 22 .0 3.65 x 10

NRU U-l and U-2: 13 3 .25" Pressure Tube 3.32 x 1012 42 9.2 3.05 x 10

19 Element Fuel, U-103 “J f-y 4.07" Pressure Tube 2.29 x 10 44 13 .9 3.18 x 1013 28 Element Fuel, U-209 4.07" Pressure Tube 2.36 x 1012 56 12.3 2.90 x 1013 18 Element Fuel, U-106 12 NRX X-5 X-522 Fuel 3 .52 x 10 2.5 0.88 x 1013 12 PRTR Mk I Fuel 3.25 x 10 38 8.,64 2.81 x 1013 HPD Fuel 3.33 x 1012 52 10.5 3.52 x 1013

WR-1 Stainless Steel P.T. 3.56 x 1012 36 .4 7 .66 2.73 x 1013 Zircaloy-4 P.T. 3.52 x 1012 36.4 7.66 2.69 x 1013 T a b le 3

Effect of Fuel Enrichment

U-235 Fuel Enrichment Natural 1.25 1.5 1.65 Wt%

Flux Factor K n/cm 2s per kw/cm 12 2.265 x 1012 2.283 x 1012 2 .290 x 10 2 .294 x 1012 k /k . natural 1.0 1.008 1.011 1.013

Table 4

Fast Neutron Flux in Fast Neutron Facilities in NRX and NRU

Facility Fast Flux (>1 MeV) Typical Rod Typical Fast for 1 MW Rod Power Power Flux (>1 MeV) n/cm^s MW n/cm^ q Mk IV Creep Machine (NRX) 4.27 x 1013 0.2 0.85 x 1013 Mk VI Creep Machine (NRU) 2.34 x 1013 0.87 2.04 x 1013 Biaxial Creep Insert (U-49) 2.37 x 1013 1.1 2.61 x 1013 -12-

APPENDIX 1

1. Cross Section Data The energy group structure and the effective absorp­ tion cross-sections for the 26 groups above 1 MeV are shown in Table Al. The energy shown is the lower energy bound of each group and the effective absorption cross-sections are the sum of the absorption and inelastic scattering cross­ sections for all materials except U-238. For U -238, the absorption cross-section only is included and the inelastic scattering cross-sections are given in detail (Table A3).

The effective scattering cross-sections are shown in Table A2. These are the transport cross sections for all materials except deuterium, hydrogen, carbon and oxygen, for which they are the scattering cross-sections. TPORT is set equal to 1 in the program, so that the scattering cross sections for deuterium, hydrogen, carbon and oxygen are automatically trans­ formed into transport cross-sections.

The total inelastic scattering cross-sections of U-238 are given in Table A3 together with the inelastic scattering cross-section for each of the 26 groups in the order shown in (14). It was assumed that all inelastic scatterings except those in U-238 lead to degradation of neutron energy to below lMeV.

The program actually used 51 energy groups between 0.1 and 10 MeV but only the first 26 groups (above 1 MeV) are necessary to calculate the fast neutron flux (>1 MeV). It should be noted, however, that if the program is run using only the 26 groups above 1 MeV, the total inelastic scattering cross-section has to be inserted. This figure is normally calculated within the program by summing the individual cross-sections for each energy group. KIN i.e., for energy group i (tot) ^ = ^E^ o\ ^ ( i, j) . KIN When the 26 groups are used, ^E^ ct^ (i,j) does not represent the total inelastic scattering cross-section since the groups below 1 MeV account for a much larger part of the total inelastic scattering cross-section than the groups above 1 MeV, as shown in Table A3.

2. Example of Geometry Data Input The geometry data input for the Douglas Point calculation is shown below in the format described in (14). -13-

DOUGLAS POINT 30011.000000 .00000 +00 1.61200 +08 0 0510000000000000000000000000000001 003101002103101101103103101101101103103001114114001117114002120120120120120120 120120120120 .3000 .7620 .9000 1.1220 1.6000 2.1780 2.4000 2.6439 2.9000 3.5000 3.7360 3.8500 4.1275 4.2600 4.3900 4.5212 5.0000 5.3848 5.5093 6.0000 6.5000 7.0000 7.5000 8.0000 8.5000 9.000010.000011.000012.000012.8973 306 .021245000 11 .042490000 14 .004110000 8 .050627000 11 .025313000 14 .042270000 11 .000010000 8 .066207000 11 .033103000 , 7 3 4 0 . 7 3 4 0 . 0 0 0 0 . 0 0 0 0 .7988 .7988 . 0 0 0 0 .0000 1.0000 1.0000 1 . 0 0 0 0 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 .0000 .0000 . 0 0 0 0 .0000 . o o o c I . 0 0 0 0 . 0 0 0 0 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 .0000 .0000 . 0 0 0 0 . 0 0 0 0 . 2 3 3 6 3 . 2 4 8 4 0 . 4 2 8 4 8 . 6 6 7 1 5 1 . 1 3 6 4 8 1 . 5 7 9 2 7 2 . 2 0 5 3 1 2 . 9 2 2 6 5 3 . 6 7 3 6 3 5 . 0 0 9 8 1 5 . 0 9 2 5 4 7 . 4 4 4 7 2 6 . 9 6 7 9 0 8 . 3 8 1 6 8 8 . 2 2 4 2 4 9 . 4 9 1 8 2 8 . 5 9 2 9 9 9 . 5 4 7 4 2 1 0 . 5 5 2 2 5 8 . 5 9 4 7 9 9 . 1 8 4 6 3 9 . 7 6 8 4 6 8 . 5 7 1 6 9 8 . 9 4 0 0 3 7 . 3 9 4 0 0 7 . 5 8 2 0 4 6 . 9 5 7 0 0 6 . 2 6 3 7 4 5 . 5 1 9 9 1 5 . 5 3 2 9 8 4 . 7 3 2 5 6 4 . 3 1 1 9 0 3 . 8 8 2 2 8 3 . 4 4 9 7 8 3 . 3 9 3 8 7 2 . 5 9 1 1 0 2 . 8 9 7 4 6 2 . 1 2 0 1 9 2 . 0 6 7 1 5 1 . 6 7 6 4 2 1 . 6 2 8 8 9 1 . 2 6 4 9 4 1 . 2 2 7 3 4 1 . 1 8 5 S 0 . 8 5 9 6 1 . 8 3 1 7 6 . 8 0 1 5 7 . 6 4 3 0 0 . 6 1 8 4 4 . 4 7 5 7 3 . 4 5 7 7 1

3. Normalization for 1 kw/cm Fuel Power

^ A modification to the program enabled DIFFCO to be used to give a flux printout for a fuel power of 1 kw/cm. DIFFCO was evaluated as follows: The energy transferred to the coolant in the fuel channel

= 194 MeV/fission -13 = 194 x 1.6 x 10 watts/fission

..• l1 1kw - : 1C)3 — ■------— f i • s s i o n s 194 x 1.6 x 10

2.438 x 103 ■13 neu^r°ns (assuming 5% fast fission ratio) 194 x 1.6 x 10'

Total number of neutrons in the source = 932.4 n/cm3 for normalization to 1 kw/cm fuel power,

194 x 1.6 x 10 13 (932.4 x ttR 2 ) CELL' For Douglas Point, R = 12.8973 CELL O DIFFCO = 1.612 x 10 Table Al

Effective Absorption Cross-Sections in barns

Lower Energy U-235 U-238 Deuterium Hydrogen Carbon Oxygen Aluminum Iron Zirconium MeV

10.0 2.8 2 .8 .0 .0 .39 .7 1.0 1.4 1.73 9.1 2.85 2 .46 .0 .0 .4 .62 .99 1.4 1.73 8.3 2.9 2 .34 .0 .0 .335 .62 .97 1.39 1.72 7.6 2 .9 2.1 .0 .0 .435 .48 .94 1.38 1.71 6.9 2 .91 1.63 .0 .0 .245 .28 .92 1.37 1.70 6.3 3 .0 .99 .0 .0 .27 .205 . 88 1.36 1.69 5.75 3 .04 .63 .0 .0 .23 .05 .85 1.36 1.69 5 .25 3 .13 .59 .0 .0 .1 .01 .81 1.35 1.68 4.8 3 .2 .57 .0 .0 .04 .110 .78 1.34 1.65 4.35 3.24 .58 .0 .0 .0 .050 .73 1.38 1.62 4.0 3.28 .58 .0 .0 .0 .09 .69 1.45 1.59 3.6 3 .3 .58 . 0 .0 .0 .01 . 65 1.4 1.54 3 .3 3.31 .58 .0 .0 .0 .0 .59 1.1 1.49 3.0 3.31 .58 .0 .0 .0 .0 .53 1.02 1.43 2.75 3.3 .59 .0 .0 .0 .0 .47 .81 1.34 2.5 3.3 .61 .0 .0 .0 .0 .4 .9 1.22 2.3 3 .29 .61 .0 .0 .0 .0 .33 .89 1.02 2.1 3.25 .61 .0 .0 .0 .0 .28 .85 .8 1.9 3 .16 .62 .0 .0 .0 . 0 .22 .67 .66 1.75 3 .05 .59 * 0 .0 .0 .0 .18 .61 .56 1.6 2 .97 .48 .0

sH .0 in .0 .0 .13 .58 .49 2 . 87 .38 .0 .0 .0 .0 .1 .61 .42 1.325 2 .82 .24 .0 .0 .0 .0 .05 .47 .34 1.2 2.73 .17 .0 .0 .0 .0 .01 .4 .27 1.1 2.68 .0 . .21 0 .0 . 0 .0 .46 .22 1 . 0 2.62 .25 .0 .0 .0 . 0 .0 .38 .15 T a b le A2

Effective Scattering Cross-Sections in barns

Lower Energy U-235 U-238 Deuterium Hydrogen Carbon Oxygen Aluminum Iron Zirconium MeV

10.0 .62 .54 .60 .47 .40 .39 .23 .27 .38 9.1 .61 .56 1.10 .98 .43 .41 .25 .31 .42 8.3 .61 .59 1.18 1.06 .44 .44 .26 .36 .49 7 .6 .64 .63 1.25 1.14 .78 .52 .31 .40 .56 6.9 .69 .69 1.32 1.22 .81 .72 .36 .44 .64 6.3 .72 .76 1.42 1.31 .51 .64 .41 .51 .68 5.75 .79 .82 1.50 1.40 .92 .89 .46 .58 .72 5.25 .85 .90 1.60 1.52 1.02 .90 .57 .63 .78 4.8 .92 .97 1.69 1.60 .80 1.18 .68 .70 .88 4.35 .98 1.05 1.78 1.72 1.15 1.28 .86 .81 .95 4.0 1.05 1.10 1.86 1.81 1.84 1.48 1.00 .88 1.07 3 .6 1.16 1.20 1.96 1.92 2.24 2.43 1.09 .93 1.18 3.3 1.34 1.36 2 .08 2.05 2.31 3.06 1.21 1.11 1.27 3.0 1.55 1.56 2 .15 2 .18 1.81 1.74 1.42 1.20 1.43 2 .75 1.72 1.71 2 .25 2.32 2.46 .82 1.62 1.25 1.57 2.5 1.80 1.79 2.35 2.45 1.69 .86 1.67 1.43 1.76 2 .3 1.79 1.79 2.43 2.58 1.56 . 66 1.68 1.44 1.93 2.1 1.80 1.76 2 .51 2.70 1.61 1.02 1.71 1.54 2.18 1.9 1.74 1.74 2.58 2.88 1.78 1.50 1.75 1 .73 2 .42 1.75 1.74 1.76 2.65 3.05 1.74 1.80 1.78 1.57 2.62 1.6 1.75 1.82 2.69 3.15 1.85 2.39 1.87 1.65 2.78 1.45 1.77 1.90 2 .75 5.35 1.96 2.00 1.88 1.71 3 .01 1.325 1.80 2.02 2 .83 3 .50 2 .06 2 .22 1.95 1.70 3.19 1.2 1.86 2.10 2 .85 3 .75 2.20 3.20 1.90 1.86 3 .45 1.1 1.94 2 .24 2.90 3.90 2.31 3.51 2.02 1.41 3.66 1.0 2.04 2.40 2.93 4.10 2.41 4.97 2.11 1.65 3.91 Table A3 U-238 Inelastic Scattering Cross-Sections, in barns

Lower Energy U-238 Inelastic Scattering Cross- Sections in Order ct(2,2) t ct (2 3) . . . a. (Total) m MeV . . . . a (2, 26) 0(3,3) ------ct(3» 26) ; etc

9.1 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .001 .001 .002 .003 .335 .003 .005 .006 .008 .007 .010 .014 .014 .017 .015 .017 8.3 .000 .000 .000 .000 .000 .000 .000 .000 .001 .002 .002 .003 .003 .004 .475 .006 .008 .011 .009 .014 .019 .020 .024 .021 .024 7.6 .000 .000 .000 .000 .000 .000 .001 .001 .002 .002 .004 .005 .006 .009 .761 .013 .016 .014 .021 .030 .031 .037 .034 .038 6.9 .000 .000 .000 .000 .000 .001 .001 .002 .002 .005 .007 .009 .013 .019 1.248 .024 .022 .033 .046 .048 .058 .053 .048 6.3 .000 .000 .000 .000 .001 .001 .003 .003 .006 .008 .012 .018 .027 .035 1.948 .032 .048 .068 .072 .086 .079 .091 5.75 .000 .000 .000 .001 .001 .002 .002 .005 .009 .012 .020 .030 .040 .037 2.368 .056 .080 .085 .102 .093 .108 5.25 .000 .000 .000 .001 .001 .001 .004 .007 .011 .020 .030 .040 .037 .057 2 .478 i .081 .087 .104 .095 .111 I-* 4.8 .000 .000 .000 .000 .000 .003 .006 .010 .019 .029 .039 .036 .056 .081 2.538 I .087 .104 .096 .112 4.35 .000 .000 .000 .000 .003 .005 .008 .017 .027 .037 .034 .054 .079 .084 2.581 .101 .093 .110 4.0 .000 .000 .000 .002 .004 .006 .015 .024 .033 .031 .050 .075 .081 .097 2.609 .089 .106 3 .6 .000 .000 .001 .002 .003 .012 .021 .030 .028 .047 .070 .076 .093 .085 2.619 .103 3 .3 .000 .000 .001 .001 .009 .018 .026 .025 .044 .066 .072 .088 .082 .099 2.631 3.0 .000 .000 .000 .008 .015 .023 .022 .039 ,061 .067 .083 .077 .094 2.640 2.75 .000 .000 .007 .013 .019 .018 .035 .055 .061 .076 .071 .088 2 .617 2.5 .000 .005 .011 .016 .015 .030 .049 .056 .069 .065 .082 2.597 2.3 .004 .008 .012 .011 .050 .072 .076 .092 .084 .102 2.569 2.1 .005 .008 .008 .069 .094 .097 .115 .104 .123 2.547 1.9 .004 .004 .089 .117 .119 .138 .124 .144 2 .509 1.75 .001 .109 .139 .139 .160 .144 .165 2 .495 1.6 .101 .128 .128 .147 .131 .1'87 2 .499 1.45 .105 .105 .120 .108 .217 2.446 1.325 .080 .091 .082 .252 2 .447 1L2 .056 .051 .278 2.398 1.1 .017 .283 2.240 1.0 .258 2.098 APPENDIX 2

Relationship between JkdG and Bundle Linear Power (P)

Jkd0 for a fuel element is evaluated by Robertson( ) as :

where q is the linear power of the element

I (xa) - 1 ) o______I (1/2) *a. I1 (*a)j a geometrical factor which depends on the fuel size and enrichment. The value of this factor'for UC>2 fuel is shown in Fig. 13.

The calculation of P from Jkd0 for a Pickering fuel bundle is given as an example:

The power distribution in a Pickering fuel bundle is such that an element in the outer fuel ring provides 3.97% of the total bundle power, and the outer element heat rating is Jkd0 = 41.8 w/cm.

From Fig. 13 the geometry and enrichment factor for natural U02, 0.6" O.D. = 0.993.

Jkd0 = ~ x [p x

P = 317 x Jkd0 = 317 x 41.8 w/cm

P = 13.25 kw/cm. -18-

APPENDIX 3

Flux Factor K for U-l and U-2 Pressure Tubes after Interpolation

Coolant 3 .25" Tube 4.07" Tube 4. 07 " Tube Density 19 Element Fuel^a^ 28 Element Fuel(£>) 18 Element Fuel(G) gm/cc K n/cm2s per kw/cm K n/cm^s per kw/cm K n/cm2 s per kw/cm

1 2 .90xl012 2 .14xl012 2 .12xl012 12 .75 3 .04xl012 2.26x10 2.23xl012

.5 3 .18xl012 2 .40xl012 2 .36xl012 12 .25 3 .34xl012 2 .55x10 2.50xl012 12 .05 3.48xl012 2 .69x10 2.62x10 12

(a) Interpolation used operating data for the period November 1965 to January 1966 during the U-103 ph II fuel experiment. (Exp-NRU-103 06.)

(b) Interpolation used operating data for the period June to September 1966 during the U-209 fuel experiment. (Exp- NRU-20901.)

(c) Interpolation used operating data for the period January to April 1967 during the U-106 and U-110 fuel experiments (Exp-NRU-10604 and Exp-NRU-11004.) -19-

APPENDIX 4

(a) Fast Neutron Flux Calculations for NRU Creep Test Ru-5

The power distribution in a fuel rod is given by:

P = P cos —TTX - x max H

where H is the extrapolated core height. The average power for a rod length L is therefore:

L/2 r p cos —- _ T . / , H

n Uli . ave X 2H i.e., P = —------. max , ttL sin 2H ..

For an NRU fast neutron rod, L = 1 4 5 cm and H = 360 cm

p i i x 1 4 5 p _ ave X 2x360

max . t t x 1 4 5 s m —2x360 r

= 1.065 x P ave

Fraction of power produced in the centre 1 4 5 cms of a. standard NP.tl fuel rod (length 274 cms) =

7 2 . 5 P ^ cos —t t x sm . ————t t x 7 2 . 5 - 7 2 . 5 max H 360

1 3 7 ^ ttx . t t x 1 3 7 P cos •—r s m • 1 3 7 max H 3 6 0

= 0.63. -20-

Total average power of surrounding rods during test period = 1.5 MW Average power from fast neutron rod during Ru-5 = 0.87 MW

power from actual rods surrounding site _ 1.5 x .63 power from 6 identical rods “ 6 x 0.87 .18.

Flux factors from EPITHET are

• 12 Adjacent rods identical K = 3.59x10 Adjacent rods zero power K = 3.07x1012

12 By interpolation K = [3.07 + .18 (3.59-3 .07)] x 10

K = 3.16xl012.

The fast neutron flux >1 MeV is given by

§ = K x P

For Ru-5 with an average power of 0.87 MW

$* _= 3.16o i x„ 10nn12 x 1.065n x ------0.87 x 103 145

$ = 2.04 x 1013 x n/cm2s.

(b) Flux Factors for NRX Creep Machine

K n/cm2s per kw/cm

Adjacent Rods Identical 8.21xl012

Adjacent Rods Zero Power 7.76x10 12

From temperature scans,

power from actual rods surrounding site power from 6 identical rods

By interpolation,

K =[7.76 + 0.75 (8.21-7 .76)] x 1012

= 8.10 x 101 2 . - 21 -

APPENDIX 5

Calculation of Fast Neutron Flux in the Biaxial Creep Insert

K n/cm^s per kw/cm

Adj acent Rods Identical 3.62xl012

Adj acent Rods Zero Power 3 .16x10 12

Using average rod powers during the first and second periods of operation:

power from actual rods surrounding site _ ^ power from 6 identical rods ~ ' "

By interpolation,

K = [3.16 + 0.14 (3.62-3.16)] x 1012 12 = 3.22 x 10 .

For 1 MW rod power,

P = 1.065 P (From Appendix 4) max ave

= 1.065 x 1

= 1.065 MW _ , , 1.065 x 10 „ _ , , P kw/cm = ------3 = 7.35 kw/cm

Fast flux >1 MeV,

$ = K x P

= 3.22 x 1012 x 7.35

= 2.37 x 10^3 n/cm^s. -22-

,G AS GAP

CALANDRIA TUBE COOLANT RINGS

PRESSURE TUBE

FUEL RINGS (U02+ Zr)

FIG. I CANDU FUEL HOMOGENIZED FOR USE IN COMPUTER PROGRAM

.CALANDRIA TUBE 0.050" WALL 4.0" I.D. (NPD) 4. 24" I. D. (DOUGLAS POINT)

AIR GAP

ZIRCALOY-2 PRESSURE TUBE 3,25" I.D. 0. 165" WALL

U02 FUEL ELEMENT 0. 6 " 0. D. D20 COOLANT 251 ° C (NPD) 271° C (DOUGLAS POINT)

FIG. 2 NPD AND DOUGLAS POINT FUEL AND PRESSURE TUBE ZIR C A LO Y - 2 CALANDRIA TUBE

FIG. 3 PICKERING FUEL AND PRESSURE TUBE

ZIRCALOY- 2

FIG. 4 GENTILLY FUEL AND PRESSURE TUBE -24-

280°C

FIG. 5 S.G. H.W.R FUEL AND PRESSURE TUBE

ALUMINUM CALANDRIA Zr - 2 .5 % Nb TUBE PRESSURE TUBE 4.566" I.D. 4.07" I.D. 0.057" WALL 0.100" WALL

AIR H20 COOLANT 280° C

FIG. 6 NRU LOOP WITH 28 ELEMENT FUEL -25-

COOLANT DENSITY gm/cc

FIG. 7 3.25" PRESSURE TUBE . 19 ELEMENT FUEL -26-

COOLANT . DENSITY gm/cc

FIG. 8 4.07" PRESSURE TUBE. 28 ELEMENT FUEL -27-

COOLANT DENSITY gm/cc FIG. 9 4.07" PRESSURE TUBE. 18 ELEMENT FUEL -28-

ZIRCALOY-2 WATER JACKET OUTER SHEATH 4.65" I.D. Si FUEL ELEMENT 0.040" WALL 0.6" 0. D. a l u m in u m CALANDRIA TUBE 5.5" I.D. 0.250" WALL Zr- 2.5 % Nb WATER JACKET INNER SHEATH 4.07" I.D. 0.110" WALL GAS GAP

WATER JACKET 30 °C

ZIRCALOY FUEL CARRIAGE Zr-2.5% Nb PRESSURE TUBE 3.25" I.D. 0.095" WALL .

FLOW TUBE 2.45" I.D. I20 COOLANT 0.075" WALL 220° C

FIG. 10 NRX X-5 LOOP WITH X*522 FUEL EXPERIMENT

ALUMINUM CALANDRIA

HB 40 COOLANT 350° C 3 0 % HB FIG. II WR-1 FUEL AND PRESSURE TUBE BIAXIAL TEST SPECIMENS

FIG. 12 NRU FAST NEUTRON ROD WITH BIAXIAL CREEP TEST INSERT '/g * a I , ( x a ) o 9- dne sldU2 yidr. Rtae fo Fg 2 EL87 (1959) 2(15)J AECL-807 Fig. from ^Retraced 95-s cylinders. for U02 solid dense, iue 3 Te eedne of dependence The 13. Figure h. xa . [h Ua)iIo . 1 1- 1 (xa)j I ndaee ad enrichment and diameter on 0 04 1 I Additional copies of this document may be obtained from Scientific Document Distribution Office Atomic Energy of Canada Limited Chalk River, Ontario, Canada

Price - $1.00 per copy

3655-68