ML19114A321
| ML19114A321 | |
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| Site: | 07103052 |
| Issue date: | 03/05/2019 |
| From: | Willems T TN Americas LLC, Orano USA |
| To: | Division of Spent Fuel Management |
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| DOS-18-011415-027-NPV, Rev. 1.0 | |
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TN International CHAPTER 2-APPENDIX 2 TN-MTR Names Signatures Date Prepared by T. WILLEMS Ref. DOS-18-011415-027-NPV Rev. 1.0 Form: PM04-3-MO-3 rev. 2 Page 1/33 NON PROPRIETARY VERSION THERMAL ANALYSIS UNDER ACCIDENT CONDITIONS OF TRANSPORT TABLE OF CONTENTS REVISION STATUS
SUMMARY
- 1. INTRODUCTION
- 2. ASSUMPTIONS MADE
- 3. MODELLING
- 4. CALCULATION CASES
- 5. RESULTS
- 6. CONCLUSION
- 7. REFERENCES LIST OF TABLES LIST OF FIGURES
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 2 / 33 NON PROPRIETARY VERSION REVISION STATUS Revision Date Modifications Prepared by /
Reviewed by Old reference: DOS-16-00173678-201 2
N/A Document first issue. Revision number intentionally set to correspond to the source document revision number.
TWI / APA New reference: DOS-18-011415-027 1.0 N/A New reference due to new document management system software.
TWI / APA
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 3 / 33 NON PROPRIETARY VERSION
SUMMARY
This document presents a thermal analysis of the TN-MTR packaging under accident transport conditions (ACT).
It aims to determine:
- maximum component temperatures and to verify that they are acceptable considering their limiting values,
- the temperature of the internal cavity to be considered for the thermal analysis of the contents under accident transport conditions, presented in Chapter 2A.
The assumptions are as follows:
- Deformations to the packaging body after the drop tests are negligible (see Chapter 1). The geometry of the body in the thermal model is as defined in Chapter 0.
- the shock absorbing cover is recessed at the trunnion under accident transport conditions as a result of the 1 m drop on a bar;
- the packaging is assumed to be in the horizontal position during the cooling phase;
- the maximum internal thermal power in the packaging is conservatively assumed to be 5500 W for the calculations. In the calculation model, this power is distributed throughout the upper part of the basket volume over a height of 599 mm;
- the basket is assumed to be centred in the cavity and placed on the bottom of the packaging, The influence of the radial gap is evaluated with a special calculation case in which the gap is assumed to be zero during and after the fire phase;
- maximum temperatures of the different components are maximised by taking account of the circumferential gradient on the area of the packaging with fins;
- ambient temperature and sunlight exposure conditions are as defined by the IAEA regulations in reference <1>. The ambient temperature is thus assumed to be equal to 38°C. Sunlight exposure is conservatively applied for 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> / day;
- under accident transport conditions, during the fire phase, the conductivity of the resin decreases linearly in order to simulate its combustion;
- the gas used to fill the cavity is conservatively assumed to be air.
The calculation of temperatures in the packaging under accident transport conditions with a conservative internal thermal power of 5500 W shows that:
- the maximum temperature of seals (201.1°C) is less than the allowable limiting value of 220°C, which guarantees leak-tightness of the containment after the accident transport conditions have terminated;
- the maximum temperature of the lead (225.8°C) is well below its melting temperature (327°C) which validates assumptions made for the calculation of the intensity of radiation around the packaging (Chapter 4A) during accident conditions.
Moreover, the temperature of the internal cavity to be considered for the thermal analysis of the contents under accident transport conditions presented in Chapter 2A in this file, is 183.8°C.
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 4 / 33 NON PROPRIETARY VERSION
- 1. INTRODUCTION This document presents the thermal analysis of the TN-MTR packaging under accident transport conditions as defined in the IAEA regulations in reference <1> and evaluates maximum component temperatures.
It is checked that these temperatures are compatible with the allowable limits.
- 2. ASSUMPTIONS MADE The main assumptions are as follows:
- Deformations to the packaging body after the drop tests are negligible (see Chapter 1A). The geometry of the body in the thermal model is as defined in Chapter 0.
- the shock absorbing cover is recessed at the trunnion as a result of the 1 m drop on a bar.
- the packaging is in the horizontal position during the cooling phase. This position is the worst position, according to <4>.
- the characteristics of the fire and ambient conditions after the fire are as defined in IAEA regulations in reference <1>: fire lasting 30 min at 800°C then ambient temperature of 38°C conservatively assuming 24 hour2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />s/day exposure to sunlight,
- the maximum internal thermal power in the packaging is conservatively assumed to be 5500 W for the calculations. In the calculation model, this power is applied throughout the upper part of the basket volume over a height of 599 mm. The basket is assumed to be in contact with the lid to maximise the temperature of the seals;
- during the fire phase, the conductivity of the resin decreases linearly in order to simulate its combustion;
- the basket-cavity radial gap is taken equal to 2 mm (the same as for normal transport conditions, see Appendix 2-1). The influence of the radial gap is evaluated with a special calculation case in which the gap is assumed to be zero during and after the fire phase;
- temperatures of packaging components are maximised by taking account of the circumferential gradient present on the area with fins;
- initial conditions before the fire correspond to normal transport conditions (see Appendix 2-1).
- 3. MODELLING 3.1 Software used The models, calculations and post-processing are made using the design and CAD code in reference <2>.
3.2 Geometry and meshing The analysis of regulatory drop tests shows that strains in the packaging body are small. Therefore these strains are neglected and the geometry of the packaging body in the thermal model is the geometry presented in Chapter 0.
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
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 5 / 33 NON PROPRIETARY VERSION geometry and the mesh of the digital model are shown in figures 2-2.1 and 2-2.2 respectively.
The packaging body is modelled by the following elements (from the inside to the outside):
an internal enclosure made of stainless steel, a layer of lead shielding, a layer of resin thermal insulation, an external enclosure made of stainless steel, a stainless steel flange positioned on the top of the body to hold the lid.
The junction between the bottom and the shell on the outside is in the form of a truncated cone.
The calculations are made with a 1/4 model due to geometric symmetries and boundary conditions.
The fins are not represented. However, their influence in convective exchanges is taken into account by applying a correction factor to the convective exchange factor.
The lid is modelled by the lead layer and the outer metal enclosure.
The stiffener shell and the orifices are not modelled.
The shock absorbing cover is modelled by its plates and its different wood grades.
The shock absorbing cover is recessed at the trunnions during and after the fire test, as a result of the 1 m drop on a bar. Therefore radiation and convection exchanges occur on this surface. The conservatism of taking account of the puncture chimney has been demonstrated in the technical note in reference <4>.
The puncture considered in the calculation model for which the results are analysed below is extremely conservative. The puncture hole did not pass through the entire thickness of the shock absorbing cover during the 1 m drop on a bar with impact on the top shock absorbing cover (drop No. 6 presented in Chapter 1-6). At the end of the drop, the remaining intact thickness of the shock absorbing cover is 61 mm, forming a non-negligible thermal protection under fire conditions. Therefore this thickness was ignored in the calculations presented below.
Moreover, considering the fact that a quarter-model is used, adding the chimney is equivalent to considering the presence of 2 chimneys in the cover, which maximises the heat flux input during the fire.
The bottom is no longer considered to be adiabatic during and after the fire (see chapter 2-1) and therefore it is subject to radiation and convection exchanges.
During the fire phase, the conductivity of the resin decreases linearly in order to simulate its combustion.
3.3 Properties of materials Material properties are presented in Table 2-2.1.
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 6 / 33 NON PROPRIETARY VERSION 3.4 Circumferential gradient methodology A circumferential gradient should be considered in the area of the packaging with fins, allowing for the packaging being in the horizontal position during cooling. The circumferential gradient in the area of the packaging with fins in the horizontal position is determined in three steps as described below:
3.4.1 First step A calculation is made on the 3D model of the packaging under steady state conditions using the boundary conditions of the transport accident conditions model in the horizontal position, to determine maximum and average surface temperatures of the area with fins at thermal equilibrium at the hottest section.
3.4.2 Second step A calculation is made on a 2D thermal << slice >> model of the hottest section of the surface of the area with fins. The objective is to determine the
<< equivalent >> power applied to the cavity wall to take account of axial heat losses, in order to obtain the maximum surface temperature of the area with fins obtained during the first step.
3.4.3 Third step A calculation is made on a 2D fluid << slice >> model using the power determined in the previous step. The average surface temperature of the area with fins determined in the first step is refitted on this model, by adjusting a multiplication factor of the exchange coefficient called the "Kh factor". The temperature difference obtained between the maximum surface temperature of the area with fins and the average temperature of this surface is taken to be the conservative value of the circumferential gradient.
The geometry of the 2D thermofluid model is shown in figure 2-2.3 and its mesh is shown in figure 2-2.4 3.5 Thermal boundary conditions Thermal boundary conditions applied in the 3D models of the packaging are shown in figure 2-2.5.
3.5.1 Conduction Heat exchanges by conduction are calculated directly by the code <2> inside the model based on the thermal properties of the materials.
Conductive exchanges through gaps in the model are fixed using conductive thermal couplings determined as follows:
ij gas ij e
C Where:
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 7 / 33 NON PROPRIETARY VERSION
- gas the thermal conductivity of the medium (air in this case), in W/m/K (see Table 2-2.1),
- eij the distance separating the 2 surfaces considered, in m,
- Cij the conductive thermal coupling in W/m²/K.
All values of the different gaps present in the model that are modelled by an equivalent exchange coefficient are given in figure 2-2.6 and are summarised in table 2-2.2.
3.5.2 Convective heat transfer coefficient on the outer surface of the package 3.5.2.1 During the fire phase The convective heat transfer coefficient during the fire test is 10 W/m2/K. This coefficient is applied to the area of the packaging without fins, the shock absorbing cover, the truncated cone, the bottom of the packaging, the handling trunnions and the surfaces of the shock absorbing cover in the punctured zone.
In the area with fins, this coefficient is applied to the developed area of the fins, which is conservative because this effectively means that the efficiency of the fins is assumed to be 1. Since the fins are not modelled, this is equivalent to applying the following convective exchange coefficient to the area with fins:
h = 10 x (Sdeveloped / Ssmooth) where:
- Ssmooth = x 1.48 x 1.12 = 5.21 m2
- Sdeveloped = x 1.48 x 1.12 + 2 x 96 x 0.06 x 1.12 = 18.11 m2 Therefore h = 34.8 W/m2/K on the area with fins.
3.5.2.2 During the cooling phase The packaging is in the horizontal position during the cooling phase.
Convection applied to cylindrical horizontal surfaces without fins is taken into account by means of the convection coefficient taken from <3> and is in the form:
h = 1.4 x T1/3 W/m2/K The presence of fins is taken into account using the same correction factor as that calculated in Chapter 2-1 and derived from Chapter 2-1-1. The convective heat exchange coefficient used on the area with fins is then:
h = (1.4 x K) x T1/3 = (1.4 x 2.93) x T1/3 = 4.1 x T1/3
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 8 / 33 NON PROPRIETARY VERSION Convection applied to the bottom of the packaging is taken into account by means of the coefficient taken from <3> and is in the form:
h = 1.28 x T1/3 W/m2/K Convection applied to plane surfaces of the trunnion is taken into account by means of the coefficient taken from <3> and is in the form:
h = 1.51 x T1/3 W/m2/K Convection applied for surfaces of the punctured area is taken into account by means of the coefficient taken from <3> and is in the form:
h = 1.22 x T1/3 W/m2/K 3.5.3 Radiation Radiative heat exchanges are considered, firstly for outer surfaces facing the ambient air and secondly through internal gaps in the model.
The net radiated flux exchanged between two surfaces i and j is calculated using the simplified equation below:
ij = Fgij (Ti 4-Tj
- 4) Si The grey view factor values used in this model between two surfaces are given by the following formulae:
1 1
1 1
j i
ij Fg
Where i and j are the emissivities of the two facing surfaces i and j.
For radiation to ambient air, the emissivity of air is assumed to be equal to:
0.9 during the fire phase; and 1 during the cooling phase and before the fire phase.
Radiative heat exchanges between the outer surfaces of the package (including the punctured area) and ambient air are calculated directly by the Code <2> using a radiative box during the cooling phase.
During the fire phase, radiative exchanges are modelled using a radiative box in the punctured area and by radiative coupling for other external surfaces.
The emissivities of the materials are given in table 2-2.1.
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 9 / 33 NON PROPRIETARY VERSION All the various radiative gaps used in the model are summarised in table 2-2.2.
3.5.4 Sunlight exposure During the fire phase, sunlight exposure is considered to be zero.
After the fire phase, sunlight exposure is conservatively applied during 24h/24. Regulatory sunlight exposure is set at:
- 0 W/m2 for plane horizontal surfaces facing downwards,
- 800 W/m2 for plane horizontal surfaces facing upwards,
- 200 W/m² for vertical surfaces,
- 200 W/m2 for other (non-horizontal) surfaces facing downwards,
- 400 W/m² for all other surfaces, Sunlight exposure on the model is presented in figure 12-2.5.
The solar flux density absorbed by the outer surface is equal to the sunlight exposure multiplied by the absorptivity of the surface, = E.
The absorption capacities of the materials are listed in Table 2-2.1.
3.6 Ambient temperature In accordance with the requirements in IAEA <1>, the ambient temperature is 38°C before and after the fire and is equal to 800°C throughout the duration of the fire (30 mn):
At t = 0 s T = 38°C At t = 30 s T = 800°C At t = 1830 s T = 800°C At t = 1860 s T = 38°C At t =
T = 38°C 3.7 Heat power The maximum thermal power of the radioactive content that can be transported in TN-MTR is 5000 W. However, maximum temperatures are conservatively determined in this chapter for a power of 5500 W.
In the model, power is applied to the homogeneous medium representing the active part of the basket (with an active height of 599 mm), as defined in Chapter 2.
The axial gap between the content and the lid is assumed to be zero during and after the fire, to maximise the temperature of the seals.
- 4. CALCULATION CASES 4.1 Initial situation Before the calculation simulating the fire test, temperatures are defined considering the package under normal transport conditions in thermal equilibrium for an
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 10 / 33 NON PROPRIETARY VERSION ambient temperature of 38°C and regulatory sunlight exposure conditions (considered for a duration of 24h/24h).
This calculation is presented in Appendix 1 in Chapter 2 in this file.
The main assumptions are summarised below.
the shock absorbing cover is not damaged, the packaging is in the vertical position.
the basket is radially centred in the cavity and placed on the bottom of the packaging, 4.2 Under accident conditions of transport Two calculation cases are carried out for accident transport conditions to determine the influence of the basket-shell gap:
In case 1, the basket-shell radial gap is identical to the value assumed for normal transport conditions, namely 2 mm.
In case 2, the basket-shell radial gap is assumed to be zero.
Furthermore, the circumferential gradient present on the area of the packaging with fins in the horizontal position is determined using the methodology presented in
§3.4. Maximum temperatures of the different packaging components are then corrected to take account of this gradient.
- 5. RESULTS Models and calculations are archived as described in reference <6>.
5.1 Calculation of the circumferential gradient 5.1.1 1st step: 3D model The following table gives maximum and mean temperatures obtained when the different components present in the hottest section of the surface of the area with fins are at thermal equilibrium under accident transport conditions for the two cases dealt with.
Components gap between basket / shell 2 mm gap between basket / shell 0 mm Tmax
(°C)
Tmean
(°C)
Tmax
(°C)
Tmean
(°C)
Outer surface of the shell with fins 107.3 106.6 107.6 107.0 Outer shell 113.5 107.6 113.8 108.0 Resin Lead 167.2 163.8 170.7 166.8 Internal cavity 167.9 166.3 172.2 170.4
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 11 / 33 NON PROPRIETARY VERSION Cavity inside surface area 167.7 166.7 172.2 171.1 Refitting is made on the maximum temperature of the outside surface of the shell with fins equal to 107.6°C, obtained for the case in which the basket /
shell gap is 0 mm.
5.1.2 2nd step: 2D thermal calibration model The following table gives maximum and mean temperatures of the different components present in the hottest section of the surface of the area with fins under accident transport conditions in the horizontal position, at thermal equilibrium after a fire.
Components Tmax
(°C)
Tmean
(°C)
Outer surface of the shell with fins 107.7 107.7 Outer shell 109.8 108.7 Resin Lead 296.1 291.0 Internal cavity 298.6 297.3 Cavity inside surface area 298.6 298.6 The power necessary to refit the maximum temperature of the outside surface of the shell with fins is 6220 W/m.
5.1.3 3rd step: 2D thermofluid model The mean temperatures of the 2D thermal and 2D fluid models are compared to validate the fluid model.
Components Tmean fluid
(°C)
Tmean thermal
(°C)
T
(°C)
Outer surface of the shell with fins 107.7 107.7 0
Outer shell 108.7 108.7 0
Resin Lead 290.9 291.0 0.1 Internal cavity 297.3 297.3 0
Cavity inside surface area 298.6 298.6 0
The value of the exchange multiplication factor Kh necessary to refit the mean temperature of the outside surface of the shell with fins is 3.24.
There is no difference between the thermal model and the fluid model, which validates the fluid model.
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 12 / 33 NON PROPRIETARY VERSION The influence of the circumferential gradient is evaluated by comparing the maximum temperatures obtained from the fluid model and those obtained from the thermal model.
Component Tmax fluid
(°C)
Tmax thermal
(°C)
T
(°C)
Outer surface of the shell with fins 116.9 107.7
+ 9.2 Outer shell 118.8 109.8
+ 9.0 Resin Lead 296.8 296.1
+ 0.7 Internal cavity 299.4 298.6
+ 0.8 Cavity inside surface area 299.4 298.6
+ 0.8 It is seen that the impact of the circumferential gradient for the most sensitive components, namely the seals (for which the temperature gradient is associated with the gradient of the internal cavity) and lead, is small (less than 1°C).
5.2 3D model under accident transport conditions in the horizontal position with puncture chimney 5.2.1 3D model The following table gives the temperatures of the main packaging components under accident transport conditions Components ACT - basket / shell gap 2 mm ACT - basket / shell gap 0 mm TMax
(°C)
Time necessary for the maximum temperature to be reached (103 s)
TMax
(°C)
Time necessary for the maximum temperature to be reached (103 s)
Outer surface of the shell with fins 718.3 1.8 718.3 1.8 Outer surface of the shell (away from area with fins) 713.8 1.8 713.8 1.8 Outer surface of the truncated cone 713.8 1.8 713.8 1.8 Resin Lead 223.1 2.0 225.1 2.0 Cavity wall (bottom) 192.0 17.0 189.7 15.0 Cavity wall (shell) 180.4 50.0 183.0 10.0 Lid inner seal 200.3 2.4 200.1 2.4
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 13 / 33 NON PROPRIETARY VERSION Components ACT - basket / shell gap 2 mm ACT - basket / shell gap 0 mm TMax
(°C)
Time necessary for the maximum temperature to be reached (103 s)
TMax
(°C)
Time necessary for the maximum temperature to be reached (103 s)
Orifice plug inner seals 189.8 50.0 185.8 50.0 Packaging isotherms are shown in figure 2-2.7 and temperature variation curves in figure 2-2.8.
5.2.2 Circumferential gradient taken into account The following table gives the temperatures of the main packaging components under accident transport conditions, taking account of the circumferential gradient:
Components ACT - basket / shell gap 2 mm ACT - basket / shell gap 0 mm Maximum temperature
(°C)
Maximum temperature with circumferential gradient
(°C)
Maximum temperature
(°C)
Maximum temperature with circumferential gradient
(°C)
Outer surface of the shell with fins 718.3 718.3 + 9.2 =
727.5 718.3 718.3 + 9.2 =
727.5 Outer surface of the shell (away from area with fins):
713.8 713.8 + 9.0 =
722.8 713.8 713.8 + 9.0 =
722.8 Outer surface of the truncated cone 713.8 713.8 + 9.0 =
722.8 713.8 713.8 + 9.0 =
722.8 Resin Lead 223.1 223.1 + 0.7 =
223.8 225.1 225.1 + 0.7 =
225.8 Cavity wall (bottom) 192.0 192.0 + 0.8 =
192.8 189.7 189.7 + 0.8 =
190.5 Cavity wall (shell) 180.4 180.4 + 0.8 =
181.2 183.0 183.0 + 0.8 =
183.8 Lid inner seal 200.3 200.3 + 0.8 =
201.1 200.1 200.1 + 0.8 =
200.9 Orifice plug inner seals 189.8 189.8 + 0.8 =
190.6 185.9 185.9 + 0.8 =
186.4
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 14 / 33 NON PROPRIETARY VERSION 5.2.3 Determination of conservative maximum component temperatures The conservative maximum temperatures of the main packaging components are determined and given in the following table, based on the 2 calculation cases under accident transport conditions and the circumferential gradient:
Components Maximum temperature
(°C)
Limit value
(°C)
Outer surface of the shell with fins 727.5 Outer surface of the shell (away from area with fins) 722.8 Outer surface of the truncated cone 722.8 Resin Lead 225.8 327 Cavity wall (bottom) 192.8 Cavity wall (shell) 183.8 Lid inner seal 201.1 220 Orifice plug inner seals 190.6 220 These results show that the maximum temperatures of the different packaging components remain less than their maximum allowable values.
The maximum temperature of the inner cavity of the uninterrupted section of the packaging is 183.8°C.
The resin temperature () is far above its limiting value of use
(). This is why criticality studies (Chapter 5A) and the calculation of the radiation intensity around the packaging (Chapter 4A) conservatively assume that the resin disappears completely during accident transport conditions.
- 6. CONCLUSION The calculated temperatures in the packaging under accident transport conditions, as defined by the regulations <1>, with a conservative internal thermal power of 5500 W show that:
- the maximum temperature of seals (201.1°C) is less than the allowable limiting value of 220°C, which guarantees leak-tightness of the containment after the fire test under accident transport conditions has terminated;
- the maximum temperature of the lead (225.8°C) remains below its melting temperature (327°C) which validates assumptions made for the calculation of the intensity of radiation around the packaging (Chapter 4A) during accident conditions.
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 15 / 33 NON PROPRIETARY VERSION Moreover, the temperature of the internal cavity to be considered for the thermal analysis of the contents under accident transport conditions presented in Chapter 2A in this file, is 183.8°C.
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 16 / 33 NON PROPRIETARY VERSION
- 7. 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> HEAT TRANSMISSION, by W. H. Mc ADAMS (French version translated by A.
BEAUFILS, second edition, DUNOD Paris 1964).
<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 puncture >> date 13/04/2011.
<5> Introduction to heat transfer - Incorpera and DeWitt - Edition Wiley - 1996
<6> Archiving of calculations:
EMC001171T / Thermal / Erreur ! Nom de propriété de document inconnu.
Model: TN_MTR Section FE model FE study Description TN-MTR 3D model with damaged shock absorbing cover NCT FIRE COOLING 3D model of the TN-MTR packaging equipped with the MTR 52S basket used for calculations under normal and accident transport conditions. The basket is homogeneous The shock absorbing cover and the trunnions are represented.
The shock absorbing cover is punctured under accident transport conditions.
Model 2D Slice in area with fins THERMAL THERMOFLUID 2D model slice of the hottest section in the area with fins used to calculate the circumferential gradient.
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 17 / 33 NON PROPRIETARY VERSION LIST OF TABLES Table Description Pages 2-2.1 Thermal properties of the materials used in the packaging 2
2-2.2 Summary of gaps modelled in the TN-MTR packaging 1
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 18 / 33 NON PROPRIETARY VERSION LIST OF FIGURES Figure Description Pages 2-2.1 Geometry of the model 3
2-2.2 Model meshing 1
2-2.3 Geometry of the 2D thermofluid model 1
2-2.4 Mesh of the 2D thermofluid model 1
2-2.5 Boundary conditions for the model 2
2-2.6 Details of modelled conductive and radiative couplings 1
2-2.7 Packaging temperature fields 2
2-2.8 Variation of the maximum temperature of the main components under accident transport conditions 1
TN International DOS-06-00032593-201 Rev. 2 Page 19 / 33 NON PROPRIETARY VERSION TABLE 2-2.1 (1/2)
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 + 6.86 x 10-5 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-18-011415-027-NPV Rev. 1.0 Page 20 / 33 NON PROPRIETARY VERSION TABLE 2-2.1 (2/2)
THERMAL PROPERTIES OF PACKAGING MATERIALS Characteristics of air (thermofluid model)
- the conductivity of air is given by the following relation: = 0.025 + 6.86. 10-5 x T (T in °C)
- the density of air is given by the following relation: =
T 026 353 (T in K)
- the following table gives values of the specific heat and viscosity as a function of the temperature in K (values derived from <5>).
Temperature (K)
Specific heat capacity (J/kg/K)
Dynamic viscosity (kg/m/s) 250 1006 1.596.10-5 300 1007 1.846.10-5 350 1009 2.082.10-5 400 1014 2.301.10-5 450 1021 2.507.10-5 500 1030 2.701.10-5 550 1040 2.884.10-5 600 1051 3.058.10-5 650 1063 3.225.10-5 700 1075 3.388.10-5 750 1087 3.546.10-5 800 1099 3.698.10-5 850 1110 3.843.10-5 900 1121 3.981.10-5 950 1131 4.113.10-5 1000 1141 4.244.10-5 1100 1159 4.490.10-5
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 21 / 33 NON PROPRIETARY VERSION TABLE 2-2.2
SUMMARY
OF GAPS MODELLED IN THE TNMTR PACKAGING Component i / j Direction Gap
[mm]
Fgij Filling gas Shock absorbing cover / Lid Axial 6 in the zone that is not punctured 0.176 Air 0 in the punctured zone Shock absorbing cover /
Lid Radial 1
0.176 Air Basket / Shell Radial 2 for the first calculation 0.111 Air 0 for the second calculation Basket / Lid Axial 0
0.176 Air Lid / puncture chimney Axial Perfect contact
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 22 / 33 NON PROPRIETARY VERSION FIGURE 2-2.1 (1/3)
GEOMETRY OF THE MODEL Packaging body PROPRIETARY PROPRIETARY
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 23 / 33 NON PROPRIETARY VERSION FIGURE 2-2.1 (2/3)
GEOMETRY OF THE MODEL Trunnion
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 24 / 33 NON PROPRIETARY VERSION FIGURE 2-2.1 (3/3)
GEOMETRY OF THE MODEL Shock absorbing cover punctured
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 25 / 33 NON PROPRIETARY VERSION FIGURE 2-2.2 MODEL MESHING Model with shock absorbing cover punctured
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 26 / 33 NON PROPRIETARY VERSION FIGURE 2-2.3 GEOMETRY OF THE 2D THERMOFLUID MODEL Component thicknesses:
Inner shell: 20 mm Lead:
Resin:
Outer shell: 25 mm
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 27 / 33 NON PROPRIETARY VERSION FIGURE 2-2.4 MESH OF THE 2D THERMOFLUID MODEL
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 28 / 33 NON PROPRIETARY VERSION FIGURE 2-2.5 (1/2)
BOUNDARY CONDITIONS FOR THE MODEL Accident transport conditions during the fire phase Convection with ambient air:
h = 10 W/m2/K (all surfaces outside the area with fins, including punctured area) h = 34.8 W/m2/K (all external surfaces of the area with fins)
Sunlight exposure:
None during the fire Radiation:
Fgij = 0.735 where outer surface = 0.8 Total dissipated power:
5500 W distributed through the equivalent homogeneous volume
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 29 / 33 NON PROPRIETARY VERSION FIGURE 2-2.5 (2/2)
BOUNDARY CONDITIONS FOR THE MODEL Accident transport conditions during the cooling phase Convection with ambient air:
h = 1.28 (T) 0.33 Sunlight exposure:
200 W/m² where = 0.9 Radiation:
Fgij = 0.8 where steel = 0.8 Convection with ambient air:
h = 1.22 (T) 0.33 Sunlight exposure:
400 W/m² where = 0.9 Radiation:
Fgij = 0.8 where steel = 0.8 Convection with ambient air:
h = 1.51 (T) 0.25 Sunlight exposure:
800 W/m² where = 0.9 Radiation:
Fgij = 0.8 where steel = 0.8 Convection with ambient air:
h = 1.28 (T) 0.33 (on cylindrical surfaces) h = 1.51 (T) 0.33 (on horizontal surfaces)
Sunlight exposure:
200 or 400 W/m² where = 0.9 Radiation:
Fgij = 0.8 where trunnions = 0.8 Convection with ambient air:
h = 4.1 (T) 0.33 Sunlight exposure:
400 W/m² where = 0.9 Radiation:
Fgij = 0.8 where steel = 0.8 Convection with ambient air:
h = 1.4 (T) 0.33 Sunlight exposure:
400 W/m² where = 0.9 Radiation:
Fgij = 0.8 where steel = 0.8 Total dissipated power:
5500 W distributed through the equivalent homogeneous volume
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 30 / 33 NON PROPRIETARY VERSION FIGURE 2-2.6 DETAILS OF MODELLED CONDUCTIVE AND RADIATIVE COUPLINGS ACT symb ol Exchange considered General significance IR radiation value of the view factor between the two walls Conduction Value of the gap in mm between the two walls (gas)
Basket / Shell 0.111 2 or 0 mm depending on the case (Air)
Basket / Lid 0.111 0 mm Shock absorbing cover / Shell 0.176 1 mm (Air)
Shock absorbing cover / Lid (punctured zone) 0.176 0 mm Shock absorbing cover / Lid (outside punctured zone) 0.176 6 mm (Air)
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 31 / 33 NON PROPRIETARY VERSION FIGURE 2-2.7 (1/2)
PACKAGING TEMPERATURE FIELD ACT, basket / shell gap = 2 mm Packaging at Tmax seals (t = 2400 s)
Packaging at Tmax lead (t = 2000 s)
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 32 / 33 NON PROPRIETARY VERSION FIGURE 2-2.7 (2/2)
PACKAGING TEMPERATURE FIELD ACT, basket / shell gap = 0 mm Packaging at Tmax seals (t = 2400 s)
Packaging at Tmax lead (t = 2000 s)
TN International DOS-18-011415-027-NPV Rev. 1.0 Page 33 / 33 NON PROPRIETARY VERSION FIGURE 2-2.8 VARIATION OF THE MAXIMUM TEMPERATURE OF THE MAIN COMPONENTS UNDER ACCIDENT TRANSPORT CONDITIONS Basket / shell gap at 2 mm Basket / shell gap at 0 mm PROPRIETARY PROPRIETARYPROPRIETARY PROPRIETARY