ML19114A320
| ML19114A320 | |
| Person / Time | |
|---|---|
| Site: | 07103052 |
| Issue date: | 03/05/2019 |
| From: | Willems T TN Americas LLC, Orano USA |
| To: | Division of Spent Fuel Management |
| Shared Package | |
| ML19115A128 | List:
|
| References | |
| DOS-18-011415-026-NPV, Rev. 1.0 | |
| Download: ML19114A320 (18) | |
Text
TN International CHAPTER 2-APPENDIX 1.1 TN-MTR Names Signatures Date Prepared by T.WILLEMS Ref.
DOS-18-011415-026-NPV Rev. 1.0 Form: PM04-3-MO-3 rev. 2 Page 1/18 NON PROPRIETARY VERSION RESULTS OF THE THERMAL TEST REPORT UNDER TRANSPORT CONDITIONS TABLE OF CONTENTS REVISION STATUS
SUMMARY
- 1.
INTRODUCTION
- 2.
PACKAGING CALCULATION MODEL
- 3.
EVALUATION OF CONVECTION COEFFICIENTS
- 4.
VERIFICATION OF INTERNAL TEMPERATURES
- 5.
RESULTS
- 6.
SUMMARY
OF RESULTS
- 7.
CONCLUSION
- 8.
REFERENCE LIST OF TABLES LIST OF FIGURES
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 2 / 18 NON PROPRIETARY VERSION REVISION STATUS Revision Date Modifications Prepared by /
Checked by Old reference: DOS-16-00173678-211 0
N/A Document first issue.
TWI / APA New reference DOS-18-011415-026 1.0 N/A New reference due to new document management system software.
TWI / APA
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 3 / 18 NON PROPRIETARY VERSION
SUMMARY
The aim of this study is to analyse the results of the thermal test carried out on the full scale TN-MTR packaging in transport configuration, instrumented with thermocouples and containing heaters to simulate the heat power of the fuel assemblies.
The purpose is to validate the assumptions of the theoretical calculations presented in the thermal analysis of the safety file, particularly concerning heat exchange coefficients.
The analysis of the thermal test guarantees that the results of the thermal analysis presented in the safety file are conservative. These findings validate the heat exchange coefficients assumed for the calculations and the value of the conductivity of the resin.
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 4 / 18 NON PROPRIETARY VERSION
- 1. INTRODUCTION The aim of this study is to analyse the results of the thermal test carried out on the full scale TN-MTR packaging in transport configuration, instrumented with thermocouples and containing heaters to simulate the heat power of the fuel assemblies <1>.
The purpose is to validate the assumptions of the theoretical calculations presented in the thermal analysis in Chapter 2 and its appendices, particularly concerning heat exchange coefficients.
This study is supported by the results of the thermal test made on the packaging and assembled in the report <1>.
NOTE: The following notation is used below for temperatures:
- << T >> = temperature in Kelvin,
- << t >> = temperature in °C
- 2. PACKAGING CALCULATION MODEL The procedure used to make the verifications summarised above is as follows:
a) The real parameters (convection, conduction, radiation) that govern heat exchanges between the ambient surroundings and the packaging cavity wall are recalculated based on test results obtained at an ambient temperature of 17°C (section 3.2.1) and for an internal power of 8000 W.
b) Packaging temperatures under normal transport conditions (ambient temperature 38°C and regulatory sunlight exposure, internal power 5500 W) are recalculated based on the coefficients thus determined.
c) These results are then compared with the values obtained in Chapter 2-1.
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 5 / 18 NON PROPRIETARY VERSION
- 3. EVALUATION OF CONVECTION COEFFICIENTS 3.1 Formulation Convection coefficients were evaluated using the following formula:
P = [h1 (T1 - T0)1.333 +
4 0
4 1
2 1
T (T
1
1
1
)] x S1 + [h2 (T2 - T0)1.333 +
4 0
4 2
2 1
T (T
1
1
1
)] x S2+ [h3 (T3 - T0)1.333 +
4 0
4 3
2 1
T (T
1
1
1
)] x S3
- T0: Ambient temperature
- T1: Surface temperature in the area without fins directly under the shock absorbing cover
- T2: Surface temperature in the area with fins
- T3: Surface temperature in the area of the truncated cone:
- h1: Convection coefficient in the area without fins directly under the shock absorbing cover
- h2: Convection coefficient in the area with fins
- h3: Convection coefficient in the area of the truncated cone:
- S1: Exchange area in the area without fins directly under the shock absorbing cover
- S2: Exchange area in the area with fins
- S3: Exchange area in the area of the truncated cone:
- : Boltzman's constant = 5.67x10-8 W/(m2 K4)
- 1: Emissivity of the Packaging
- 2: Emissivity of the ambient air
- P: Internal thermal power 3.2 Evaluation of coefficients 3.2.1 Ambient temperature t0 The value of 38°C is used for calculations under normal transport conditions (see Chapter 2 and appendices). This value is different for tests. Reference
<1> states that the maximum temperature reached after the ambient temperature thermocouple reaches equilibrium is equal to 17°C.
t0 = 17°C
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 6 / 18 NON PROPRIETARY VERSION 3.2.2 Convection coefficients h1, h2 and h3 Coefficient h2 on wall with fins The coefficient h2 is determined using the following relation derived from reference <3>:
h2 = h1 x K where:
K =
L n x x
1
n = 96 (number of fins)
L = 2 x 60 + 3 = 123 mm (developed length of fins)
= x 1480 (perimeter at the base of the fins in mm)
=
H
)
H
(
th
H = 60 mm
.e
.L e)
.2.(L
)
T (T
ail ail 0,333 0
1 1
h Lfin = 1120 mm e= 3 mm
= 16 W.m-1.K-1 (thermal conductivity of the steel in the fins)
Coefficients h1 and h3 on smooth wall h3 = h1 3.2.3 Emissivity of the packaging1 1 = 0.3 (see chapter 0) 3.2.4 Ambient emissivity 2 = 1
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 7 / 18 NON PROPRIETARY VERSION 3.2.5 Heat power The installed thermal power at thermal equilibrium is 8000 W. We will use this as reference value:
P = 8,000 W 3.2.6 Heat exchange area The heat exchange area is calculated assuming that the packaging is a 1240 mm high 1480 mm diameter cylinder plus a tapered conical area located at the bottom of the packaging calculated as shown in figure 1. The exchange area is divided into 3 parts:
S1: area without fins located between the fins and the shock absorbing cover S1 = x 1.480 x 0.12 = 0.56 m2 S2: area with fins (area of the cylinder at the bottom of the fins)
S2 = x 1.480 x 1.12 = 5.21 m2 S3: area of the truncated cone S3 = 0.67 m2 (see figure 1)
The temperature given by thermocouples TEX1 and TEX9 (outside surface of shock absorbing cover see <1>) increases to a much lesser extent than the temperature measured on the surface of the packaging. Thus, the shock absorbing cover acts as thermal insulation, and therefore the heat flux passing through the shock absorbing cover can be assumed to be negligible.
==
Conclusion:==
The heat exchange area with the ambient air is composed only of the cylindrical part (area with fins + area without fins) and the tapered part of the packaging.
3.3 Evaluation of h as a function of temperatures given by the tests h1 is the unknown in the following equation:
P = [h1 (TEX2 - T0)1.333 +
4 0
4 2
2 1
(
1 1
1 T
TEX
)] x S1+
[h1 x K (TEX3 - T0)1.333 +
4 0
4 3
2 1
(
1 1
1 T
TEX
)] x S2+
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 8 / 18 NON PROPRIETARY VERSION
[h1 (TEX5 - T0)1.333 +
4 0
4 5
2 1
(
1 1
1 T
TEX
)] x S3 P = 8 000 W
<1>
T0 = 273 + 17 = 290 K
<1>
TEX2 = 273 + 102 = 375 K <1>
TEX3 = 273 + 79 = 352 K <1>
TEX5 = 273 + 77 = 350 K <1>
S1 = 0.56 m2 S2 = 5.21 m2 S3 = 0.67 m2 1 = 0.3 2 = 1 Solving this equation gives:
h1 = h3 = 1.718 SI K = 2.925 h2 = h1 x K = 5.025 SI 3.4 Proportion of flux exchanged through each area Area without fins The flux exchanged through the area without fins is written:
P1 = [h1 (TEX2 - T0)1.333 +
4 0
4 2
2 1
(
1 1
1 T
TEX
)] x S1 P1 = 480.6 W which is 6.0% of the total power (8000 W).
Area with fins The flux exchanged through the area with fins is written:
P2 = h1 x K (TEX3 - T0)1.333 +
4 0
4 3
2 1
(
1 1
1 T
TEX
)] x S2
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 9 / 18 NON PROPRIETARY VERSION P2 = 7158.6 W which is 89.5% of the total power (8000 W).
Tapered area The flux exchanged through the tapered area is written:
P3 = [h1 (TEX5 - T0)1.333 +
4 0
4 5
2 1
(
1 1
1 T
TEX
)] x S3 P3 = 360.8 W which is 4.5% of the total power (8000 W).
- 4. VERIFICATION OF INTERNAL TEMPERATURES This step refits the value of thermal conductivity of the resin based on the results obtained during the test. This is done by determining the temperature gradients in the various successive layers of materials located between the packaging cavity and the exterior starting from temperatures recorded during the test on the outside surface of the packaging (TEX3) and on the internal wall of the cavity (TB7). These factors will then be used (Section 5) to refit the temperatures assuming an outside temperature of 38°C.
4.1 Notation R4 = 500 R1=740 R2=
R3=
basket shell Resin Outer enclosure cavity PACKAGING SECTION lead R5 = 480 T1, t1: Temperature on the surface of the packaging.
T2, t2: Temperature on the outer face of the resin.
T3, t3: Temperature on the outer face of the lead.
T4, t4: Temperature on the inner face of the lead.
T5, t5: Temperature of the inner face of the cavity
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 10 / 18 NON PROPRIETARY VERSION 4.2 Determination of t2 The gradient in the outer shell is determined:
t2 = P R + t1 where R =
2 1
acier R
R ln L
2 1
t1 = TEX3 =79°C (see <1>)
steel = 16 W/m°C R1 = 740 mm R2 =
L = 1240 mm (height of part with fins + height of part without fins = 1120 mm +
120 mm)
P = 8000 W t2 =
1 2
1 acier t
R R
ln L
2 P
t2 =
4.3 Determination of t4 t4 =
ln 2
5 4
5 R
R L
P t
acier
t5 = TB7 = 133°C (see <1>)
L = 1080 mm (height of cavity)
R4 = 500 mm R5 = 480 mm steel = 16 W/m°C, P = 8000 W t4 = 130.0°C 4.4 Determination of t3 t3 =
4 3
4 ln 2
R R
L P
t plomb
L = 1240 mm, R3 =
R4 = 500 mm lead =
32 W/m°C P = 8000 W t3 =
4.5 Determination of resin
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 11 / 18 NON PROPRIETARY VERSION resin =
3 2
2 3
ln
)
(
2 R
R L
t t
P
L = 1240 mm, R2 =
R3 =
t3 =
t2 =
P = 8000 W resin =
This value is very close to the value used for the calculations in Chapter 2-1
().
4.6 Summary of temperatures from t1 to t5 t1 = 79°C t2 =, giving a gradient in the outer enclosure:
t2 = t2 - t1 =
t3 =, giving a gradient in the thickness of the resin:
t3 = t3 - t2 =
t4 = 130.0°C, giving a gradient in the thickness of the lead:
t4 = t4 - t3 =
t5 = 133°C, giving a gradient in the thickness of the inner shell:
t5 = t5 - t4 = 3°C The real conductivity of the resin is obtained from these temperature gradients:
resin =
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 12 / 18 NON PROPRIETARY VERSION
- 5. RESULTS The temperatures tna, tsc, tsa corresponding to the temperature of the area without fins, the temperature of the tapered area and the temperature of the area with fins respectively, and temperatures t2 to t5 are calculated for an ambient temperature of 38°C, to compare them with the results of the calculations in Chapter 2-1. The internal power is 5500 W and allowance has to be made for sunlight exposure. It is assumed that the proportion of flux exchanged by each packaging area remains constant. Table 1 describes the verification that the same flow type is present (in fact turbulent conditions) under transport conditions and under test conditions.
t0 = 38°C or T0 = 311 K Area without fins Tna solution of:
)
T (T
1
1
1
)
T (T
h
S P
4 0
4 na 2
1 1,333 0
na 1
solaire 1
1
where:
56
,0 6
5500 1
1
S P
(see section 3.4) solar = 200 W/m2 (see Chapter 2 and Appendices)
= 5.67 x 10-8 W/m2 K4 1 = 0.3 2 = 1
= 0.4 absorptivity of stainless steel h1 = 1.71 SI tna = 106.3°C Tapered area Tsc solution of:
)
T (T
1
1
1
)
T (T
h
S P
4 0
4 sc 2
1 1,333 0
sc 1
solar 3
3
where:
67
,0 5,4 5500 3
3
S P
(see section 3.4) solar = 200 W/m2 (see Chapter 2 and Appendices)
= 5.67 x 10-8 W/m2 K4 1 = 0.3 2 = 1
= 0.4 absorptivity of stainless steel h1 = 1.71 SI
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 13 / 18 NON PROPRIETARY VERSION tsc = 88.4°C Area with fins Tsa solution of:
)
T (T
1
1
1
)
T (T
h K
S P
4 0
4 sa 2
1 1,333 0
sa 1
solar 2
2
where:
5,21 5,
89 5500 S
P 2
2
(see section 3.4) solar = 200 W/m2 (see Chapter 2 and Appendices)
= 5.67 x 10-8 W/m2 K4 1 = 0.3 2 = 1 h1 = 1.71 SI
= 0.4 absorptivity of stainless steel K = 2.93 tsa = 87.0°C The temperatures at the different levels are deduced directly from temperature gradients by conduction demonstrated in section 4.6, as follows:
t2 = tsa + t2 = 87 + x (5500 / 8000) =
t3 = t2 + t3 = + x (5500 / 8000) =
t4 = t3 + t4 = + 10.3 x (5500 / 8000) =
t5 = t4 + t5 = + 3 x (5500 / 8000) =
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 14 / 18 NON PROPRIETARY VERSION
- 6.
SUMMARY
OF RESULTS t° in°C t0 tna tsc t1 = tsa t2 t3 t4 t5 Results recalculated following the analysis of the test 38 (h1 = 1.716 h2 =5.02 )
106.3 88.4 87.0 Results of chapter 2-
- 1.
38 (h1 = 1.7 h2 = 5) 105.9 103 91.2
/
149.2 154.7 Where:
t0:
Ambient temperature.
tna:
Surface temperature of the area without fins tsc:
Temperature of the truncated area t1=tsa: Temperature of the area with fins t2:
Outside limit of the resin t3:
Inside limit of the resin (outside of lead) t4:
Inside limit of lead t5:
Internal wall of the packaging cavity
- 7. CONCLUSION Therefore the above analysis guarantees that the results of the thermal analysis presented in Chapter 2 and its appendices are conservative. These findings validate the heat exchange coefficients assumed for the calculations and the value of the conductivity of the resin.
- 8. REFERENCE
<1> << Acceptance test report for the TN MTR transport packaging >> ARCTECH ref AF99112 date 30/10/99.
<2> << Heat Transmission >> W.H. Mc Adams, second edition, Dunod 1964.
<3> << Theoretical studies on transmission of heat >> Volume 1 by Georges RIGOT. Les
éditions parisiennes.
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 15 / 18 NON PROPRIETARY VERSION LIST OF TABLES Table Designation No. of pages 2 x 1.1 Determination of the flow condition 1
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 16 / 18 NON PROPRIETARY VERSION LIST OF FIGURES Figure Designation No. of pages 2 x 1.1 Calculation of the area of the truncated cone 1
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 17 / 18 NON PROPRIETARY VERSION TABLE 2-1-1.1 DETERMINATION OF THE FLOW CONDITION The following checks that the air flow over the outer surface of the packaging corresponds to a turbulent condition, for the calculation under transport configuration and for the calculation during the thermal test.
Flow is turbulent if 109 < Pr.Gr < 1012.
wherePr is the Prandtl number: Pr =
C Gr is the Grash of number: Gr = g
2 3
2 L
T
where:
= viscosity of the fluid C
=heat capacity of the fluid
= conductivity of the fluid g
= acceleration due to gravity,
= density of the fluid
- coefficient of expansion of the fluid L
= horizontal cylinder length T
= temperature difference between wall and fluid = tp - te Fluid properties are evaluated at the film temperature (te + tp)/2 where te is the air temperature and tp is the wall temperature.
Thus, the product Pr.Gr is written: Pr.Gr =
L T
C g
p 2
3 Values of the
p 2
C g
factor for air are obtained in <2> on page 537.
Test conditions Transport conditions Wall temperature tp (°C) 79 87 Fluid temperature te (°C) 17 38 Film temperature (°C) 48.0 62.5
p 2
C g
69.5106 57.6106 T
62 49 L (m) 1.12 1.12 Pr.Gr 6.05 x 109 3.97 x 109 It is clear that the flow is turbulent since 109 < Pr.Gr < 1012.
TN International DOS-18-011415-026-NPV Rev. 1.0 Page 18 / 18 NON PROPRIETARY VERSION Figure 2-1-1.1 CALCULATION OF THE AREA OF THE TRUNCATED CONE Consider the truncated cone defined below:
The surface area of the truncated cone is defined as follows:
)
(
2 d
D m
Scone
where:
2 2
2 h
d D
m
Therefore with:
D = 1.48 m d = 1.26 m h = 0.11 m.
m = 0.16 Scone = 0.67 m² d
D m
h