ML19114A318
| ML19114A318 | |
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|---|---|
| Site: | 07103052 |
| Issue date: | 03/05/2019 |
| From: | Lecoq A TN Americas LLC, Orano USA |
| To: | Division of Spent Fuel Management |
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| ML19115A128 | List:
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| References | |
| DOS-18-011415-024-NPV-Rev. 1.0 | |
| Download: ML19114A318 (23) | |
Text
TN International CHAPTER 2 TN-MTR Names Signatures Date Prepared by A. LE COQ Ref. DOS-18-011415-024-NPV Rev. 1.0 Form: PM04-3-MO-3 rev. 2 Page 1/23 NON PROPRIETARY VERSION THERMAL ANALYSIS OF THE PACKAGE CONTENTS
SUMMARY
- 1.
INTRODUCTION
- 2.
THERMAL CRITERIA
- 3.
PACKAGING CALCULATION MODEL
- 4.
DEFINITION OF THE CONTENT OF THE FINITE ELEMENT CALCULATION MODEL
- 5.
BOUNDARY CONDITIONS
- 6.
RESULTS
- 7.
SEAL LIFE AND FILLING RATE
- 8.
INFLUENCE OF VYAL B RESIN
- 9.
CONCLUSION
- 10. REFERENCES LIST OF TABLES LIST OF APPENDICES APPENDIX 2-1: THERMAL ANALYSIS UNDER NORMAL TRANSPORT CONDITIONS APPENDIX 2-1-1:......... RESULT OF THE TEMPERATURE TEST REPORT UNDER TRANSPORT CONDITIONS APPENDIX 2-2: THERMAL ANALYSIS UNDER ACCIDENT TRANSPORT CONDITIONS
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 2 / 23 NON PROPRIETARY VERSION REVISION STATUS Revision Date Modifications Prepared by /
Reviewed by Old reference: DOS-14-00173678-200 3
N/A Document first issue. Revision number intentionally set to correspond to the source document revision number.
ALC / TWI New reference: DOS-18-011415-024 1.0 N/A New reference due to new document management system software.
ALC / TWI
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 3 / 23 NON PROPRIETARY VERSION
SUMMARY
This document presents the thermal analysis of the TN-MTR packaging under normal and accident transport conditions as defined in the IAEA regulations in reference <1>.
The assumptions are as follows:
the geometry of the packaging body under normal or accident conditions complies with the geometry described in Chapter 0. This assumption is validated by the mechanical analysis of the packaging given in Chapter 1 and the extrapolation calculations made in Appendix 9 to chapter 1 that demonstrate that packaging deformations during the mechanical tests (and particularly the drop tests) are negligible. The packaging is modelled with its shock absorbing cover and its trunnions; under accident transport conditions, the shock absorbing cover has a recess adjacent to the trunnion corresponding to the consequences of the 1 m drop on a bar. Therefore it is considered that radiation and convection exchanges can take place through this area during the fire test and during the cooling phase; boundary conditions are conforming with the requirements in IAEA rules in reference
<1> for normal and accident transport conditions; the maximum allowable thermal power in this packaging is 5000 W but calculations are made conservatively assuming a power of 5500 W. This power is distributed in the upper part of the basket volume over a height of 599 mm in the calculation models to give maximum seal temperatures.
The analysis for normal conditions is described in chapter 2-1. The analysis of the thermal test described in Chapter 2-1-1 validates the heat exchange coefficients assumed in the calculations and the value of the conductivity of the resin. The analysis for accident conditions is described in chapter 2-2. The results are given below:
The results of these analyses are given in the following table.
Normal Conditions of Transport Accident Conditions of Transport Component Maximum temperature
(°C)
Limit value
(°C)
Maximum temperature
(°C)
Limit value
(°C)
Outer surface of the shell with fins 91.2 727.5 Outer surface of the shell (away from area with fins) 105.9 722.8 Outer surface of the truncated cone 103.0 722.8 Resin Lead 149.2 327 225.8 327 Cavity wall (bottom) 154.7 192.8 Cavity wall (shell) 117.3 183.8
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 4 / 23 NON PROPRIETARY VERSION Normal Conditions of Transport Accident Conditions of Transport Component Maximum temperature
(°C)
Limit value
(°C)
Maximum temperature
(°C)
Limit value
(°C)
Lid inner seal 114.5 160 201.1 220 Orifice plug inner seals 117.1 160 190.6 220 These results show that the maximum temperatures of the different packaging components remain less than their maximum allowable values.
Temperatures of the packaging and particularly of the cavity wall are used as input data for the thermal analysis of the content of the packaging presented in Chapter 2A and its appendices. The temperatures to be considered for the thermal analysis of the content are 117.3°C under normal transport conditions and 183.8°C under accident transport conditions.
It is also demonstrated that there is no risk of extrusion of containment seals under normal transport conditions or under accident transport conditions.
It is also demonstrated that changing from F resin to Vyal B resin has no influence on packaging temperatures under normal or accident transport conditions.
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 5 / 23 NON PROPRIETARY VERSION
- 1. INTRODUCTION This document presents the thermal analysis of the TN-MTR packaging under normal and accident transport conditions as defined in IAEA regulations <1>.
The purpose of this study is to determine maximum temperatures of the different packaging components under normal and accident transport conditions to:
- compare them with limiting temperatures for use of the materials from which the packaging is made,
- determine input data for other safety analyses.
- 2. THERMAL CRITERIA Several thermal criteria have been established for the different components of the TN MTR packaging, particularly to check that temperatures do not invalidate the assumptions made for the geometry and material properties, for confinement and criticality studies and for calculations of the dose equivalent rate around the packaging:
- the temperature of EPDM seals must not exceed 160°C under normal transport conditions or 220°C for at least 8 days under accident transport conditions. It must also be checked that the filling rate of the expanded seal in its groove does not exceed 100% under normal and accident transport conditions.
- if the resin is to remain efficient, its temperature under normal transport conditions must not exceed 150°C,
- the lead temperature must not exceed 327°C (melting temperature) under normal and accident transport conditions.
- 3. PACKAGING CALCULATION MODEL 3.1 Geometric model The geometry of the packaging body is identical under normal transport conditions and under accident conditions. The drop tests made on the mockup of the TN-MTR packaging, for which the report is presented in Appendix 6 to Chapter 1 and the extrapolation calculations made are given in Appendix 9 to Chapter 1, demonstrated that deformations on the packaging body after the regulatory drop tests are negligible.
Calculations are made using the finite elements method on a three-dimensional model in which the packaging body is modelled with its trunnions and its lid. The shock absorbing cover composed of stainless steel plates and wood is modelled.
3.2 Material properties Thermal properties of these materials are presented in Table 2.1.
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 6 / 23 NON PROPRIETARY VERSION 3.3 Packaging position The packaging is transported in the vertical position. Therefore the thermal analysis under normal transport conditions is made assuming that the packaging is in this position.
Under accident transport conditions, the packaging is in the horizontal position, which is a conservative position for the packaging as described in reference <4>.
- 4. DEFINITION OF THE CONTENT OF THE FINITE ELEMENT CALCULATION MODEL The case of the MTR 52S basket is considered arbitrarily to model the content of the packaging. The temperatures in which we are interested in this Chapter are the packaging temperatures and these depend largely on solar flux, the internal thermal load, boundary conditions and thermal properties of the different packaging materials. They are not very dependent on the basket properties. Furthermore, temperatures of the packaging content are not discussed in this chapter and are determined in Chapter 2A and its Appendices.
The model is made by distributing the thermal power in a conservative manner in the upper part of the basket volume over a height equal to 599 mm, so as to determine the manner in which the removal of thermal power is distributed and the resulting hot spots.
This is the position in which temperatures at the seals of the lid and the orifice plugs are maximum.
The cavity of the calculation model is filled by three media:
- a cylinder at the bottom of the cavity representing the inactive lower part of the assemblies,
- a cylinder located immediately above in which the power is distributed, representing the active part of the assemblies,
- an air disk representing the gap between the basket and the packaging lid, the basket being supported on the bottom of the packaging.
A height, a radial and axial thermal conductivity, a density and a specific heat are defined for each medium (see Appendix 2-1 in this Chapter).
A minimum axial gap between the basket and the lid are defined to obtain the maximum temperature on the seals.
The height of the cavity is 1080 mm and its diameter is 960 mm, according to Chapter 0.
According to Chapter 0A and its appendices, the maximum height of baskets with high thermal power, and therefore the MTR 52S, is 1071 mm. The axial basket/lid gap is therefore assumed to be 9 mm. The diameter of this basket is 956 mm, such that the radial basket/cavity gap is 2 mm.
Under accident transport conditions, the axial basket/lid gap is considered to be zero in order to maximise seal temperatures. The influence of the radial basket/cavity gap on packaging temperatures is evaluated.
- 5. BOUNDARY CONDITIONS
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 7 / 23 NON PROPRIETARY VERSION Boundary conditions applied to the packaging are different for normal and for accident transport conditions. These are specified in Chapters 2-1 and 2-2.
The internal thermal power considered is 5500 W. This power bounds the maximum allowable power according to Chapter 0A (5000W).
- 6. RESULTS The following table presents maximum packaging temperatures under normal and under accident transport conditions, taken from Chapters 2-1 and 2-2.
Normal Conditions of Transport Accident Conditions of Transport Component Maximum temperature
(°C)
Limit value
(°C)
Maximum temperature
(°C)
Limit value
(°C)
Outer surface of the shell with fins 91.2 727.5 Outer surface of the shell (away from area with fins) 105.9 722.8 Outer surface of the truncated cone 103.0 722.8 Resin Lead 149.2 327 225.8 327 Cavity wall (bottom) 154.7 192.8 Cavity wall (shell) 117.3 183.8 Lid inner seal 114.5 160 201.1 220 Orifice plug inner seals 117.1 160 190.6 220 Temperatures reached by packaging components are below their limiting temperatures of use, and in particular:
- the maximum temperature reached by the lead is 149.2°C under normal transport conditions and 225.8°C under accident conditions. These temperatures are below the melting temperature of lead (327°C)
- the maximum temperature reached by the resin is under normal transport conditions, which is less than its maximum temperature of use (). Under accident conditions, the resin temperature is and is therefore higher than the temperature of. Thus, the criticality studies (Chapter 5A) and the dose rate calculations (Chapter 4A) for accident transport conditions are made conservatively assuming complete degradation of the resin;
- the maximum temperature reached by the seals is 117.1°C under normal transport conditions, which is less than the maximum temperature of use under steady-state conditions (160°C). The maximum temperature of the seals under accident transport conditions is 201.1°C, which is less than the limiting temperature under these conditions (220°C). The life of the seals is studied in § 7.
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 8 / 23 NON PROPRIETARY VERSION Therefore for a power of 5500 W, the maximum temperature of the cavity wall is 117.3°C under NCT and 183.8°C under ACT. These temperatures should be considered for the thermal analysis of the contents presented in Chapter 2A.
- 7. SEAL LIFE AND FILLING RATE 7.1 Operational life expectancy of the seals Therefore, the temperature of EPDM seals is less than 160°C under NCT and 220°C under ACT. The following equations derived from <3> are used to estimate the life of seals in hours as a function of the temperature, for temperatures of less than 220°C:
- L (T < 220°C) =
T 8,314 317638 2
3 e
10 5,15
, for Le JOINT FRANCAIS's grade EP8517 EPDM seals
- L (T < 220°C) =
T 8,314 137314 12 e
10 00 2,
, for STACEM's grade 48DRL13 EPDM seals where L is in hours and T is in °Kelvin.
The following assumptions have been conservatively adopted:
- a duration of 1 year (365 d) under normal conditions,
- a duration of 1 week (7 d) under accident conditions,
- Le JOINT FRANCAIS's grade EP8517 EPDM seal Damage (ET) to seals is calculated:
ET (final) =
C)
(220 L
24 7
C)
(160 L
24 365 EPDM EPDM
ET (final) =
228 24 7
10 04
,1 24 365 7
= 0.74 < 1 Based on the assumptions made, the leak-tightness of the seals is guaranteed remain leak-tight since damage to seals is less than 1.
7.2 Filling rate It is checked that the filling rate of seal grooves is less than 100%, which eliminates the risk of extrusion of the seals.
The seal groove filling rate is verified for:
- containment seals,
- lid inner seal
- inner seal for the orifice A and B protective plugs
- outer seals.
- lid outer seal
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 9 / 23 NON PROPRIETARY VERSION
- outer seal for the orifice A and B protective plugs.
The seal groove filling rate is calculated as follows:
Filling coefficient =
volume groove volume seal Where:
- Seal volume =
20))
(T
(1 4
)
tore d
int (D
2 tore d
2
- Groove volume =
20))
(T (1
D
section groove area
- T: maximum seal temperature under normal and accident transport conditions The temperatures considered to calculate the seal groove filling rate are conservatively assumed to be 160°C for normal transport conditions and 220°C for accident transport conditions.
- : volume expansion coefficient of the seal
- : volume expansion coefficient of the groove
- dtorus:
torus diameter
- Dint:
inside diameter of the O-ring seal
- D:
mean groove diameter Details of the calculation are shown in table 2.2. The filling rate is calculated taking account of fabrication tolerances for the calculation of the minimum groove volume and the maximum seal volume derived from Chapter 0.
According to Chapter 0, the material of the lid and the protective plug for orifices A et B is type B. The volume expansion coefficient of the seal groove material is assumed to be equal to :
- 37.92 x 10-6 K-1 at 20°C
- 40.11 x 10-6 K-1 at 160°C
- 41.13 x 10-6 K-1 at 220°C The volume expansion coefficient for EPDM seals is 515 x 10-6 K-1, according to reference <5>.
Maximum filling rates of the volume of the seal groove calculated for the TN MTR packaging under normal and accident transport conditions are summarised in the following table:
Filling coefficient of the volume of the lid seal groove Inner seal Outer seal Normal Conditions of Transport 95.91 95.93 Accident Conditions of Transport 98.41 98.44
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 10 / 23 NON PROPRIETARY VERSION Filling rate of the volume of the groove for orifice A and B plug seals Inner seal Outer seal Normal Conditions of Transport 92.56 92.28 Accident Conditions of Transport 94.98 94.70 Values are less than 100%, which excludes all risks of extrusion of the seal.
Therefore the EPDM seals perform their confinement function perfectly.
- 8. INFLUENCE OF VYAL B RESIN This section studies whether or not the use of Vyal B type resin for which the thermal properties are different from the properties of F resin, induces a change in the global thermal behaviour of the packaging.
The important parameter under normal transport conditions is thermal conductivity. For F resin, the thermal conductivity is equal to whereas for Vyal B resin it is equal to (see Chapter 0).
The equivalent thermal resistance for a cylinder is thus expressed as follows:
i e
r r
R ln 2
1
Therefore the thermal resistance is inversely proportional to the thermal conductivity, which means that the thermal resistance will increase.
Chapter 2-1-1 shows that the temperature gradient through the resin for a thermal power of 5500W is equal to C
27 Knowing that the temperature gradient is proportional to the thermal resistance (
R T
), it is deduced that the temperature gradient will increase to C
32 with Vyal B resin.
Therefore the use of Vyal B resin instead of F resin will result in a slight increase (less than 5°C) of packaging temperatures under normal transport conditions for a thermal power of 5000 W, which is not very significant.
The important parameter under accident transport conditions is thermal diffusivity. At the beginning of a fire, the diffusivity of Vyal B resin is than that of F resin as can be seen in the following table:
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 11 / 23 NON PROPRIETARY VERSION F resin VYAL B resin Diffusivity =
p C
Therefore calculations using the properties of F resin are conservative because they increase the flux input into the packaging at the beginning of the fire.
The drop in conductivity applied to F resin during the fire materialises combustion of the resin and is applicable to Vyal B resin.
In conclusion, the presence of Vyal B resin instead of F resin does not modify the results and conclusions obtained with F resin.
- 9. CONCLUSION The calculation of temperatures in the TN-MTR packaging under conditions conforming with the requirements in the IAEA rules <1> for normal and accident transport conditions made using a 3-dimensional model, shows that thermal criteria are respected: it is shown that the maximum lead temperature remains below the melting point under normal and accident transport conditions. The resin temperature remains below its maximum usage temperature under normal transport conditions.
It is demonstrated that there is no risk of extrusion of the containment EPDM seals.
It is also demonstrated that changing from F resin to Vyal B resin has no influence on packaging temperatures under normal or accident transport conditions and that the conclusions obtained with F resin are applicable to Vyal B resin.
Packaging temperatures and particularly temperatures of the cavity wall are used as input data for the thermal analysis of the packaging content presented in Chapter 2A and its appendices for contents with a thermal power of 5500 W. Temperatures to be considered for the thermal analysis of the contents under normal and accident transport conditions are 117.3°C and 183.8°C respectively.
- 10. REFERENCES
<1> Applicable IAEA regulations: see chapter 00;
<2> NX I-DEAS 6.1 M1 finite element calculation software interfaced with the TMG 6.0.1181 thermal module and the ESC 6.0.1181 fluids module distributed by Siemens PLM software
<3> ASN/DIT/0061/2009 letter dated 28/01/2009 corrected by the TN International letter CEX-09-00136347-079 dated 28/07/2009
<4> TN International Technical note NTC-11-00032583 Rev.0, << Influence of the model of the shock absorbing cover and trunnions on the thermal analysis of the TN-MTR packaging. "Allowance for perforation >> date 13/04/2011.
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 12 / 23 NON PROPRIETARY VERSION
<5> ASN - DGSNR/SD1/0533/2005 letter July 21 2005
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 13 / 23 NON PROPRIETARY VERSION LIST OF TABLES Table Description Pages 2.1 Thermal properties of the materials used in the packaging 1
2.2 Calculation of the filling rate of containment seal grooves and outer seal grooves 1
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 14 / 23 NON PROPRIETARY VERSION LIST OF APPENDICES Figure Description Pages 2.1 Equivalent thermal properties of the basket and its content 7
TN International DOS-06-00032593-200 Rev. 3 Page 15 / 23 NON PROPRIETARY VERSION TABLE 2.1 THERMAL PROPERTIES OF PACKAGING MATERIALS Materials Thermal conductivity (W.m-1.K-1)
Emissivity Solar absorptivity Specific heat capacity (J.kg-1.K-1)
Density (kg.m-3)
Stainless steel 16 0.3 before the fire 0.4 before the fire 500 7,850 0.8 during the fire no sunshine during the fire 0.8 after the fire 0.9 after the fire Lead 32 130 11,300 Basket active zone (homogeneous environment) 3 (radial) 708 1,510 25 (axial)
Basket inactive zone (homogeneous environment) 3 (radial) 713 1,500 26 (axial)
Resin Air 0.025 +
6.86x10-5 x T T (in°C) 1 before the fire 0.9 during the fire 1 after the fire Balsa 0.05 2,092 140 Oak 0.2 0.8 during and after the fire 1,460 600 Plywood 0.1 0.8 during and after the fire 1,215 500
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 16 / 23 NON PROPRIETARY VERSION TABLE 2.2 CALCULATION OF THE FILLING RATE OF THE CONTAINMENT SEAL GROOVES AND THE OUTER SEAL GROOVES Lid Orifice A and B protective plugs Inner seal Outer seal Inner seal Outer seal GROOVE PARAMETE R
Nominal Min. Tol.
Nominal Min. Tol.
Nominal Min. Tol.
Nominal Min. Tol.
Mean diameter (D) 1130 2.4 1170 2.4 90.5 0.6 121 0.6 Opening (A) 7.2 0.05 7.2 0.05 4.8 0.05 4.8 0.05 Angle 30 30 30 30 Depth (C) 5.5 0.05 5.5 0.05 3.65 0.05 3.65 0.05 r1 0.4 0.4 0.26 0.26 r2 0.8 0.8 0.53 0.53 Volume expansion coefficient at temperature 20° 3.79E-05 3.79E-05 3.79E-05 3.79E-05 Volume expansion coefficient at temperature under NCT 4.01E-05 4.01E-05 4.01E-05 4.01E-05 Volume expansion coefficient at temperature under ACT 4.11E-05 4.11E-05 4.11E-05 4.11E-05 SEAL PARAMETE RS Nominal Min. Tol.
Nominal Min. Tol.
Nominal Min. Tol.
Nominal Min. Tol.
Inner diameter 1055 5.13 1093 5.13 81.93 0.54 111.14 0.69 Torus diameter 7.8 0.15 7.8 0.15 5
0.1 5
0.1 Grade EPDM EPDM EPDM EPDM Volume expansion coefficient 5.15E-04 5.15E-04 5.15E-04 5.15E-04 FILLING RATES Nominal
(%)
Maximum
(%)
Nominal
(%)
Maximum
(%)
Nominal
(%)
Maximum
(%)
Nominal
(%)
Maximum
(%)
Ambient temperature 20 20 20 20 Filling rate 84.5 89.96 84.5 89.98 80.15 86.82 80.09 86.56 NCT temperature 160 160 160 160 Filling rate 90.09 95.91 90.12 95.93 85.45 92.56 85.39 92.28 ACT temperature 220 220 220 220 Filling rate 92.44 98.42 92.47 98.44 87.69 94.98 87.62 94.7 The maximum filling rate of the seals is 98.44% under accident transport conditions.
Angle
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 17 / 23 NON PROPRIETARY VERSION APPENDIX 2.1 EQUIVALENT PROPERTIES OF THE BASKET AND ITS CONTENT The properties of the three media (inactive cylinder, active cylinder and air disk) are defined below.
The basket is composed of a stack of stainless steel and borated aluminium disks. It is 1071 mm high and it is distributed as follows:
- a 24 mm stainless steel disk at the bottom and the top of the basket
- a stack of 8 stainless steel disks each of which is 12 mm high and 9 borated aluminium disks each of which is 103 mm high.
The thermal properties of aluminium and stainless steel in the basket are derived from Chapter 0A-4 in this file.
Cylinder modelling the inactive part This cylinder is composed of stainless steel and aluminium disks of the basket, assemblies and air. Its height is 1071 - 599 = 472 mm.
Equivalent radial conductivity The equivalent radial conductivity is calculated by writing that the thermal power is transmitted through the stainless steel and aluminium structure of the basket. Therefore the conductivity of steel and aluminium applied to the exchange area is calculated, neglecting conductive exchanges in air.
The square cross-section of compartments in steel disks is 99 mm x 99 mm and the compartments are surrounded by 8 mm of stainless steel. There is a 2 mm thick stainless steel liner with a 94 mm x 94 mm square cross-section inside each compartment.
The square cross-section of compartments in aluminium disks is 101 mm x 101 mm and the compartments are surrounded by 6 mm of aluminium. There is a 2 mm thick stainless steel liner with a 94 mm x 94 mm square cross-section inside each compartment.
The percentage of steel or aluminium for each cylindrical section is calculated assuming 4 mm of steel or 3 mm of aluminium around each compartment. Since the number of compartments in each disk is equal to the number of metals parts, and making an approximation for projections on areas, we can write:
%steel = (2x4 + 2x2) / (99 - 2x2) = 13% for steel disks
%steel+alu = (2x3 + 2x2) / (101-2x2) = 10% for aluminium disks According to the relation for conductive exchanges in a cylinder, the amount of the flux exchanged through the steel disks is written:
Qsteel = [2 hsteelsteel (Tint-Text) / ln(rext/rint)] %steel
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 18 / 23 NON PROPRIETARY VERSION Assuming that the temperature of the steel and aluminium disks balances out, the amount of the flux exchanged through the aluminium disks is written:
Qalu = [2 halueq_alu (Tint-Text) / ln(rext/rint)] %steel+alu where:
eq_alu =
140 6
16 4
10
e
e e
alu alu acier acier totale
=34 W/m.K We can also write:
Qtotal = Qsteel + Qalu = 2 hbasket eq (Tint-Text) / ln(rext/rint)
The following radial equivalent conductivity is then calculated:
eq = [(steel x %steel) hsteel + (eqalu x %steel+alu) halu] / hinactive basket where:
hsteel: height of steel disks on the inactive part = 1 x 24 + 3 x 12 = 60 mm halu: height of aluminium disks on the inactive part = 4 x 103 = 412 mm steel: thermal conductivity of stainless steel = 16 W/m.K eqalu: thermal conductivity of aluminium + steel liner = 34 W/m.K Therefore eq = [(16 x 0.13) x 60 + (34 x 0.10) x 412] / 472 = 3 W/m.K Equivalent axial conductivity The equivalent axial conductivity is calculated by writing that the thermal power is transmitted through the stainless steel and aluminium structure of the basket, through the stainless steel liners and through the spacers or legs of the assemblies (assumed to be made of stainless steel). The equivalent conductivity is calculated neglecting conductive exchanges in air.
Basket:
The equivalent conductivity of the sequence of borated aluminium and stainless steel disks in the axial direction is:
basket =
140 412 16 60 472
e
e e
alu alu steel steel total
= 70 W/m.K
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 19 / 23 NON PROPRIETARY VERSION The volume of material (ignoring liners) in the inactive part (height 472 mm and diameter 956 mm) is:
0,103 4
101
,0 52 0,012) 3 0,024 (1
0,099 52 472
,0 0,956 4
2 2
2
=
0.0897 m3 Therefore on average, each section of the inactive part contains:
0.0897 / 0.472 = 0.190 m2 of material, namely:
%basket =
2 956
,0 4
190
,0
= 26%
Liner:
The thermal conductivity of the liners in the axial direction is equal to the thermal conductivity of stainless steel, namely liners=16 W/m.K For each section in the basket, the percentage of stainless steel due to the liners is:
%liners =
2 2
2 956
,0 4
)
094
,0 098
,0
(
52
= 6%
Assemblies:
Assemblies are taken into account by considering them to be composed of uranium and aluminium alloy plates placed between borated aluminium plates.
The corresponding thermal conductivity is determined in Chapter 2A-2 for this type of assembly and is equal to:
assemblies = 120 W / m.K It is estimated that the area of aluminium in the assembly is 10% of the section.
This value is fixed as being representative of the assemblies.
Therefore the percentage of aluminium per section is:
%assemblies =
2 2
956
,0 4
10 094
,0 52
= 6%
Based on the relation for conductive exchanges through a plane section and assuming that the temperature is uniform throughout each section:
Q
=
Stotal eq (Tint-Text) / e
=
Stotal %basket basket (Tint-Text) / e + Stotal %liners liners (Tint-Text) / e
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 20 / 23 NON PROPRIETARY VERSION Q
=
Stotal eq (Tint-Text) / e We can deduce:
eq = basket x %basket + liners x %liners + assemblies x %assemblies eq = 70 x 0.26 + 16 x 0.06 + 120 x 0.06 = 26 W/m.K Equivalent Density:
The equivalent density is calculated by the following relation:
eq = (Vbasket basket + Vliners liners + Vassemblies assemblies) / Vtotal where:
Vbasket basket = 0.190 x (7850 x 0.06 + 2700 x 0.412) = 301 kg Vliners liners = 52 x (0.0982 - 0.0942) x 0.472 x 7850 = 148 kg Vassemblies assemblies = 10% x 52 x 0.0942 x 0.472 x 2700 = 59 kg Vtotal =
472
,0 956
,0 4
2
= 0.339 m3 Hence:
eq = 1500 kg/m3 Equivalent specific heat The relation for the temperature rise of a body is:
Q = mtotal Cpeq (Tfinal - Tinitial) = [ (mi Cpi) ] (Tfinal - Tinitial)
Therefore: Cpeq = [ (mi Cpi) ] / mtotal Cpeq = (mbasket Cpbasket + mliners Cpliners + massemblies Cpassemblies) / mtotal where:
mbasket Cpbasket = 0.190 x (7850 x 0.06 x 500 + 2700 x 0.412 x 900) = 235 x 103 J/K mliners Cpliners = 148 x 500 = 74 x 103 J/K massemblies Cpassemblies = 59 x 900 = 53 x 103 J/K mtotal = 301 + 148 + 59 = 508 kg Hence:
Cpeq = 713 J/kg.K
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 21 / 23 NON PROPRIETARY VERSION Cylinder modelling the active part This cylinder is composed of stainless steel and aluminium disks of the basket, assemblies and air. It is 599 mm high.
Equivalent radial conductivity The approach is the same as for the inactive part. We then have:
%steel = (2x4 + 2x2) / (99 - 2x2) = 13% for steel disks
%steel+alu = (2x3 + 2x2) / (101-2x2) = 10% for aluminium disks and:
eq = [(steel x %steel) hsteel + (eqalu x %steel+alu) halu] / hinactive basket where:
- hsteel: height of steel disks on the active part = 1 x 24 + 5 x 12 = 84 mm
- halu: height of aluminium disks on the active part = 5 x 103 = 515 mm
- steel: thermal conductivity of stainless steel = 16 W/m.K
- eqalu: thermal conductivity of aluminium + steel liner = 34 W/m.K Therefore eq = [(16 x 0.13) x 84 + (34 x 0.10) x 515] / 599 = 3 W/m.K Equivalent axial conductivity The approach is the same as for the inactive part.
Basket:
The equivalent conductivity of the sequence of borated aluminium and stainless steel disks in the axial direction is:
basket =
140 515 16 84 599
e
e e
alu alu steel steel total
= 67 W/m.K The volume of material (ignoring liners) in the active part (height 599 mm and diameter 956 mm) is:
515
,0 101
,0 52 0,084 0,099 52 599
,0 0,956 4
2 2
2
= 0.1140 m3.
Therefore on average, each section of the active part contains:
0.1140 / 0.599 = 0.190 m2 of material, i.e.:
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 22 / 23 NON PROPRIETARY VERSION
%basket =
2 956
,0 4
190
,0
=26% of material.
Liner:
The thermal conductivity of the liners and the percentage of stainless steel due to the liners is unchanged relative to the case of the inactive part. With:
liners=16 W/m.K
%liners = 6%
Assemblies:
The thermal conductivity of the assemblies and the percentage of material that they represent in each section is unchanged relative to the case of the inactive part. With:
assemblies = 120 W / m.K
%assemblies = = 6%
It is then deduced that:
eq = basket x %basket + liners x %liners + assemblies x %assemblies eq = 67 x 0.26 + 16 x 0.06 + 120 x 0.06 = 25 W/m.K Equivalent Density:
In the same way as for the inactive part, the equivalent density is calculated by the following relation:
eq = (Vbasket basket + Vliners liners + Vassemblies assemblies) / Vtotal where:
Vbasket basket = 0.190 x (7850 x 0.084 + 2700 x 0.515) = 389 kg Vliners liners = 52 x (0.0982 - 0.0942) x 0.599 x 7850 = 188 kg Vassemblies assemblies = 10% x 52 x 0.0942 x 0.599 x 2700 = 74 kg Vtotal =
599
,0 956
,0 4
2
= 0.430 m3 Hence:
eq = 1510 kg / m3
TN International DOS-18-011415-024-NPV Rev. 1.0 Page 23 / 23 NON PROPRIETARY VERSION Equivalent specific heat In the same way as for the inactive part, the equivalent specific heat is calculated by the following relation:
Cpeq = (mbasket Cpbasket + mliners Cpliners + massemblies Cpassemblies) / mtotal where:
mbasket Cpbasket = 0.190 x (7850 x 0./084 x 500 + 2700 x 0.599 x 900) = 300 x 103 J/K mliners Cpliners = 188 x 500 = 94 x 103 J/K massemblies Cpassemblies = 74 x 900 = 67 x 103 J/K mtotal = 389 + 188 + 74 = 651 kg Hence:
Cpeq = 708 J/kg.K Summary The results of the above calculations are summarised in the following table.
Inactive cylinder Active cylinder Height [mm]
472 599 eq_radial (W/m.K) 3 3
eq_axial (W/m.K) 26 25 eq (kg/m3) 1,500 1,510 Cpeq (J/kg.K) 713 708 These values are used to model the content in the calculations.