ML22271A790
| ML22271A790 | |
| Person / Time | |
|---|---|
| Site: | Orano USA |
| Issue date: | 03/31/2016 |
| From: | TN International |
| To: | Division of Fuel Management |
| Garcia-Santos N | |
| Shared Package | |
| ML22271A128 | List:
|
| References | |
| A33010, L-2022-DOT-0007 | |
| Download: ML22271A790 (21) | |
Text
TN International APPENDIX 2.2-5 A
AREVA Names Signatures I Date FCC3-FCC4 Prepared by DOS Ref. 00081778-205- Rev 00 Checked by NPV Form: PM04-3-MO-3 rev. 2 Page 1/21 ANALYSIS OF THE IMPACT OF GLYCERINE ON THE THERMAL SAFETY ANALYSES CONTENTS
- 1. PURPOSE .......................................................................................................................... 4
- 2. INPUT DATA .................................................................................................................... 4 2.1 Residual glycerine .................................................................................................... 4 2.2 Glycerine properties ................................................................................................ 5 2.3 Thermal study overview .......................................................................................... 5
- 3. COMBUSTION OF GLYCERINE - 1ST METHOD .................................................... 7 3.1 1st phenomenon - combustion of the layer of glycerine ....................................... 7 3.2 2nd phenomenon - overall energy input .............................................................. 11 3.3 Conclusion .............................................................................................................. 12
- 4. COMBUSTION OF GLYCERINE - 2ND METHOD ................................................. 14 4.1 The thermal flux created by the flame ................................................................. 14 4.2 Calculation of rod cladding temperatures ........................................................... 15 4.3 Modelling ................................................................................................................ 16 4.4 Clearance between the pellet and cladding ......................................................... 16 4.5 Materials ................................................................................................................. 17 4.6 Boundary conditions .............................................................................................. 17 4.7 Initial temperature................................................................................................. 17 4.8 Results ..................................................................................................................... 18 Non-proprietary version
TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 2 / 21 4.9 Creep consequences ............................................................................................... 18
- 5. CONCLUSION ................................................................................................................ 20
- 6. REFERENCES ................................................................................................................ 21 Non-proprietary version
TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 3 / 21 REVISION STATUS Prepared by /
Revision Date Modifications Checked by 0 12/2015 First issue Non-proprietary version
TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 4 / 21
- 1. PURPOSE The purpose of this appendix is to analyse, for FCC3 and FCC4 package models, the impact of the presence of 5 g of glycerine on the fuel assemblies used in the studies presented in the FCC3 & FCC4 safety analysis reports covering the creep behaviour during regulatory fire conditions affecting the rods. All the thermal and creep analyses in this report, under regulatory fire conditions, are carried out using conservative assumptions, with the PWR 17x17 assembly, which covers all other types of fuel assembly, that is PWR 14x14 and PWR 15x15 assemblies. Therefore, the conclusions of this analysis on the impact of glycerine on PWR 17x17 fuel assemblies are also applicable to the other types of assembly.
Glycerine is a hydrogen-containing material, with an auto-ignition temperature (see reference <1>) less than the maximum temperature reached by the fuel rods under the regulatory fire test conditions (see present report).
During manufacturing, the glycerine, which is soluble in water, is applied to each of the rods prior to them being inserted into the assembly grids. After rinsing the assemblies with water, the residual glycerine is therefore divided among all the rods in the array.
An analysis of the risks relating to possible combustion of the glycerine in the FCC3 &
FCC4 packagings is detailed below.
This analysis justifies a scenario involving the increase in rod temperature caused by the burning of the 5 grammes of glycerine during the regulatory fire test under Accident Conditions of Transport.
Secondly, an evaluation, based upon numerical calculations, is carried out using the test results, in order to confirm that the scenario considered is consistent with the cladding temperatures.
Finally, it was shown that these scenarios have no impact on the resistance of fuel rod claddings to the phenomenon of creep.
- 2. INPUT DATA 2.1 Residual glycerine Even though the glycerine is divided among all the rods in the array and spread over the full length of the assembly, the residual glycerine is assumed, in a conservative manner, to be concentrated at one assembly grid (over a length of 44 mm -
corresponding to the width of a 17x17 PWR assembly grid) and for the whole population of rods.
This leads to the consideration that the residual glycerine on the rods accumulated at one grid when the rods were inserted into the assembly skeleton.
The following notation will be employed throughout the rest of the studies:
m = 5 g: Mass of glycerine; n = 264: Number of rods with deposits of glycerine.
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TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 5 / 21 2.2 Glycerine properties M = 92.1 g/mol: Molar mass of glycerine; Tflashpoint = 177°C: Flashpoint of glycerine; Tvap = 290°C: Vaporisation temperature of glycerine; Tautoign. = 400°C: Auto-ignition temperature of glycerine; Hcomb = 1252.4 kJ/mol: The enthalpy of the glycerine combustion reaction, from <1> (taking into account the phase change enthalpies associated with combustion reaction products and reagents).
The MTDS for the glycerine applied to the rods is in Reference <6>.
2.3 Thermal study overview The thermal analysis during fire conditions for the FCC3 and FCC4 packages is detailed in Appendix 2.2-1, supported by Appendix 2.2-2 of the Safety Analysis Report.
The heating of the rods, and in particular, the glycerine, is by a flow of hot air entering via the gaps in the door (as shown in the figure below, taken from Appendix 2.2-1 of the Safety Analysis Report).
The primary heat exchanges within the cavities of FCC3 and FCC4 packagings are convective in nature. The fluid flowrates within the upper zone of the assembly are between and m/s. The flowrates given in the figure above correspond to the start of a fire (Figures A4.18 - Appendix 2.2-1 of the Safety Analysis Report).
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TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 6 / 21 The calculations used to determine the maximum temperatures reached for the fuel rod claddings, under Accident Conditions of Transport, give temperatures of higher than 400°C for some rods.
The temperature increase curves for the hottest claddings are as follows:
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TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 7 / 21
- 3. COMBUSTION OF GLYCERINE - 1ST METHOD Using the aforementioned elements, the following scenario is used to conservatively limit the consequences of the heating caused by combustion of the glycerine.
The glycerine combustion is triggered at a temperature somewhere between the flashpoint of glycerine (177°C) and its auto-ignition temperature (400°C). Within this range, some of the glycerine vaporises within the cavity of the FCC3/FCC4 packaging (at 290°C). This creates a gas pocket.
In order to evaluate the increase in cladding temperatures, it is necessary to consider the following phenomena:
1st phenomenon: combustion of the residual layer of glycerine on the rods. This produces energy which locally heats the fuel rods, principally by means of convection and radiation (a flame in contact with the rods).
2nd phenomenon: a more generalised combustion of the glycerine within the cavity, providing a quantity of energy which may increase the temperature of the cladding and the walls of the packaging cavity.
In parallel with the combustion of the glycerine, the fire outside the packaging continues to heat the rods, according to a kinetics identical to that presented in paragraph 2.3.
However, this plays no role in the heating of the rods as it is replaced by the combustion of the layer of glycerine (1st phenomenon), where the flame temperature is much higher than the external fire.
3.1 1st phenomenon - combustion of the layer of glycerine As the residual glycerine on the rods has not had the time to vaporise because of the vaporisation kinetics of glycerine between the vaporisation and the auto-ignition temperatures, it will ignite in the worst case at 400°C.
At this temperature the layer of glycerine will start combustion. Above the surface of the glycerine will be found a zone corresponding to the escaping gases. This zone is followed by a flame, within which the gases come in contact with the oxygen in the air and combustion occurs. The temperature of this zone is considered to be 1500 K (a temperature corresponding to that of the temperature of a candle flame).
We therefore assume a flame will then be licking the other rods within the assembly and heating the rods, mainly through convection and radiation.
To quantify the effect of combustion, it is therefore necessary to:
Determine the type of flux coming in contact with the rods, in order to calculate the coefficients of convection and radiation; Evaluate the flux transmitted to the rods touched by the flame; Determine the rate of combustion of the glycerine, in order to evaluate the kinetics of the rod temperature rise.
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TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 8 / 21 3.1.1 Determining the flux coming in contact with the rods The following calculation characterises the type of flows around the rods, which is used in turn to evaluate the convective part of the heat exchange coefficient.
This calculation is notably based upon the flowrates of air through the cavities, noted in Paragraph 2.3. These flowrates are representative of those expected in the presence of the flame in contact with the hottest claddings, as these are the claddings closest to the point of entry of the flux.
Dh v D v We then evaluate the corresponding Reynolds Number: Re = h i Where:
v i , the flowrate of the air around the rods, v = m/s conservatively (see Paragraph 2.3 - the following calculations show a laminar airflow, thus, the conclusion of this laminar airflow applies to all lower flowrate),
4A Dh, Hydraulic diameter of the assembly, Dh = ;
P A, cross-sectional flow area, A = Sass - Srods; Sass, cross-section of assemblies, Sass = mm x mm ;
D 2 Srods, cross-section of rods, Srods = 264 x ;
4 D, external rod diameter, D = 9.4 mm.
Giving A = m2 And:
P, the wetted perimeter of this section, P = Pass Prods ;
Pass, perimeter of the cross-section of assemblies, Pass = mm x 4 Prods, perimeter of the rods, Prods = 264 x D.
Hence P = 8.65 m and Dh = mm and,
, the kinematic viscosity of air, = 14.5x10-5 m2/s at a temperature T.
Where:
Tflame Tcladdings T, average air temperature, T = ;
2 Tflame = 1500 - 273 = 1227°C Tcladding = 400°C (Corresponding, conservatively, to the vaporisation temperature of glycerine);
Therefore: T = 813.5°C We then deduce the corresponding Reynolds Number: Re Non-proprietary version
TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 9 / 21 For a Reynolds Number such that 40 < Re < 4000, the coefficient of convection can be determined using the following formula:
hD NuD = = 0.683 Re0.466 xPr1/3 from <3>
Where:
Cp Pr, the Prandtl number, Pr = = 0.728 for air, from <3> ;
, average conductivity of air at a temperature T, = 72.4x10-3 W/m/K 0,683 Re0,466 Pr1/3 where, h = = W.m-2.°C-1 D
The coefficient of convective heat exchange (hconv) is therefore W.m-2.°C-1 We then define the global coefficient of heat exchange hg corresponding to the sum of the coefficients of convective heat exchange (hconv) and radiative heat exchange (hrad), or: hg = hconv + hrad.
Exchanges by radiative heat represents 30% of all heat exchanges, from reference <2> (Chapter 1, Section 2).
30 Thus hg = h conv 1 = W.m-2.°C-1 70 3.1.2 Flux transmitted to the rod The heating of a cladding by a flame created by the combustion of glycerine can therefore be determined, assuming that this occurs during a period t, from an initial temperature corresponding to the vaporisation temperature of glycerine and a gas temperature at a maximum of Tflame.
In order to achieve this, conservatively we assume that the pellets play no role in the inertia of the rods.
Thus, the heat quantity balance for the cladding gives:
dT M Cp = hg S T dt dT S e Cp = hg S (Tflame - T) dt dT hg Where T T dt eCp flame t 0, T Ti 400C T Ti t
Thus, 1 e with being the time constant, Tflame Ti Non-proprietary version
TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 10 / 21
= eCp hg The cladding heating is thus expressed as:
t T = (T - Ti) = 1 e Tflame Ti Where:
Tflame = 1500 - 273 = 1227 °C,
, the density of the claddings, = 6500 kg.m-3, Cp: specific heat of the claddings, Cp = J.kg-1.K-1, e, thickness of cladding, e = 0.52 mm, hg = W.m-2.°C-1 The cladding temperature follows the following curve:
3.1.3 Rate of glycerine combustion By treating the behaviour of glycerine as identical to that of an oil, we can assume the mean mass flow rates of between m = 0.05 and 0.1 kg/s/m2, from
<2> (Chapter 1, Section 3 Heat release rate).
Knowing the thickness of the glycerine, the duration of combustion can be expressed as:
e t = gly gly m
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TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 11 / 21 Where:
gly , the density of the glycerine, gly = 1260 kg/m3
, the mass flow rate of the glycerine = 0.05 kg/s/m2 conservatively m
egly, the average thickness of the glycerine = 0.012 mm assuming 5 g of glycerine divided among 264 rods and a length of 44 mm, equivalent to the width of the grid.
Hence: t = 0.3s From the temperature rise curve above, the heating of the claddings will be at a maximum of 13°C after 0.3 s.
As the mass flow rate of the glycerine is not specifically available in established literature, mass flow rates lower than those considered may be found. This is the case of alcohols, where the mass flow rates can be 0.015 kg/s/m². In this case, the heating of the cladding will therefore be a maximum of 42.3 °C after 1 second. A mass flow rate of 0.015 kg/s/m² corresponds to the value found during a stable regime. This value is very low in so far as, for thin layers of fuel the mass flow rates are higher.
3.2 2nd phenomenon - overall energy input The combustion of glycerine releases a certain quantity of energy, heating the gases within the cavity. Taking into account the air flowrate through the cavity, these hot gases rapidly spread throughout the cavity.
Assuming a conservation of the glycerine combustion energy, the energy contained within the gases is likely to heat the rods, and the walls of the cavity in the FCC3 or FCC4 packaging.
To quantify the effects of this heating, the analysis involves:
estimating the energy released by the combustion of glycerine, determining, conservatively, the temperature delta in the rods caused by the glycerine combustion reaction.
3.2.1 Energy released by combustion The quantity of glycerine vaporising and diffusing through the array of rods in the assembly is 5 g,;it is spread across the width of a grid, i.e. 44 mm.
The energy released by the combustion of the residual glycerine is expressed in the following manner:
m H comb E comb M
Where:
m is the mass of glycerine deposited, m = 5 g Hcomb, enthalpy of the glycerine combustion reaction as defined in Paragraph 2.2, Non-proprietary version
TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 12 / 21 M, the molar mass of glycerine (See Paragraph 2.2).
3.2.2 Energy absorbed by the assembly Conservatively, we restrict the propagation of this glycerine, in gaseous form, throughout the array to mm either side of the zone in question.
We assume that all the energy released by the combustion of the glycerine is absorbed by the claddings and the walls of the internal fittings, which means ignoring the quantity of energy absorbed by the pellets in the fuel rods and by the structures of the assembly. We also ignore the quantity of the hot gases which may have been removed by the flow of air within the cavity.
The energy absorbed by the claddings and walls is then expressed in the following manner:
E abs m claddings Cp claddings n m walls Cp walls T Where:
mcladding = g, corresponding to mm ( + + mm) of cladding, with a diameter of 9.4 mm and a thickness of 0.52 mm (from Chapter 1.3 of the Safety Analysis Report),
Cpcladding = J.kg-1.K-1 (See Appendix 2.2-1 of the Safety Analysis Report for a Zr-4 cladding, corresponding to the most conservative case),
n = minimum number of rods in the array (from Chapter 1.3 of the Safety Analysis Report), n = 264, mwalls = kg, corresponding to mm of walls, with a width of 220 mm and a thickness, limited for conservative purposes, to that of the claddings (i.e. 0.52 mm),
Cpcladding = 550 J.kg-1.K-1 (See Appendix 2.2-1 of the Safety Analysis Report for stainless steel).
Assuming that Eabs = Ecomb and taking into account the minimum number of rods within the assembly (264), this gives us:
-- - I 5
T ° 264 550 The heating of the claddings will be a maximum of °C.
3.3 Conclusion Combining the two phenomena:
flame in contact with a rod for 0.3 s, Heating of the rods by the cavity gases (assuming conservation of the glycerine combustion energy),
On completion of the glycerine combustion, the temperature reached by the fuel rod claddings is a maximum of °C. This increase is represented by the curve below:
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TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 13 / 21 In the event that the duration of the glycerine combustion is 1 s, the temperature reached by the rod claddings would be a maximum of °C.
Moreover, evaluations of the transient increases (locally and throughout all the claddings) are conservative in nature as they ignore:
the leakage of the evaporated glycerine dissipated by the flux caused by the external fire through the gaps between the frame and door, the thermal degradation of the glycerine, decreasing the combustion source term, the hot combustion gases which may have been removed by the flow of air within the cavity.
The temperature of the claddings, at the end of the regulatory fire test, with the combustion of the glycerine, remains identical to that obtained without the presence of glycerine (See Paragraph 2.3): in fact, this temperature is not dependent on a transient combustion which might occur during the increase in temperature.
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TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 14 / 21 The following curve illustrates what happens during the combustion of glycerine:
Thus, the increase in temperature caused by the combustion of glycerine is produced for an extremely short transient, at a local point on the cladding. The energy is then dissipated throughout the rest of the structures (pellets, grids, doors, framework, nozzles etc.); this level of energy remains negligible with respect to the quantity of energy added by the accidental fire conditions.
- 4. COMBUSTION OF GLYCERINE - 2ND METHOD Tests were carried out in order to characterise candle flames (reference <4>). The aim of these tests was to measure several parameters linked to the combustion of a candle, more precisely to measure the maximum thermal flux emitted by a candle flame. Based upon this flux, it is possible to determine, using calculations, the corresponding increase in temperature relating to the duration of glycerine combustion.
4.1 The thermal flux created by the flame Taking into consideration the configuration of an assembly array, the rods will be at various distances from the flames. The experiment detailed in Reference <4>
describes a device used to measure the density of the thermal flux in the vicinity of a candle flame. The test is used to take measurements of the thermal flux density created by the flame, in both the horizontal and vertical plane.
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TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 15 / 21 The thermal flux density versus the radial distance and at two elevations, taken from
<4>, is presented in the figure below:
120 iHt o Vertical position. y =60 mm
"' Vertical position, y =80 mm 100 80 1 1Hi t
~c t f c::
60 ii t t 8 I
..c:
1/2 s 40 it
{:. i t
iii ii;
.! !I!
20 i!>
A41 68 6
0
-25 -15 -5 5 15 25 Radial di stance from centerline, r (mm)
Figure 9. Heat flux above the flame as a function of radial distance from the flame centerline at two vertical positions above the base of the candle using a 3-mm diameter total heat flux gauge.
The maximum flux density measurement is approximately 120 kW/m² at the flame, and at a distance from the flame of 60 mm. In the same way, the test focused on the maximum density of the thermal flux at the tip of the flame. The largest value for the flux density was measured at 145 kW/m².
We use this value (145 kW/m²) as the maximum flux density of a candle flame (considered representative of glycerine) in order to calculate the heating of the rods caused by the absorption of this heat flux generated by the flames.
4.2 Calculation of rod cladding temperatures The study involves evaluating the maximum temperature reached by the cladding of a rod in the event that the glycerine in the vicinity of the cladding catches fire and heats the latter.
The modelling includes the pellet, the surrounding cladding and a gap between the pellet and the cladding. The heat provided by the combustion of glycerine is modelled by a power, taken to be equal to 145 kW/m², on the outer surface of the cladding. The calculation is carried out for a duration of 10 seconds and the maximum cladding temperature is measured at the moment corresponding to the duration of glycerine combustion.
The assumption of applying the power to the rod cladding is extremely conservative as it means considering that the totality of the glycerine combustion energy is absorbed by the rod.
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TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 16 / 21 This study was carried out using the finite difference computer code I-DEAS/TMG
<5> to simulate thermal phenomena.
4.3 Modelling The pellet and the rod cladding are meshed using three-dimensional solid and shell elements. The characteristic dimensions are taken from Chapter 1.3 of the Safety Analysis Report, and are summarised below:
Minimum external rod diameter: 9.4 mm, Min cladding thickness: 0.52 mm, Maximum pellet diameter: 8.3 mm.
The geometry and meshing are presented below.
Pellet Cladding 4.4 Clearance between the pellet and cladding From Table 3 in Chapter 2.2-2 of the Safety Analysis Report, the radial gap between pellet and cladding is mm and a minimum of mm. Moreover, the inclusion of the differential expansions between the pellet at °C and the cladding at °C leads to a slight change in the gap at low temperature (not more than 10%) and therefore covers the value of °C. Conservatively we assume a constant gap of mm, which represents an increase in the gap of more than 90%.
This gap is modelled by a thermal coupling.
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TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 17 / 21 4.5 Materials The thermal characteristics of the model elements are taken from Chapter 2.2-1 of the Safety Analysis Report. The thermal properties of M5 are used for the digital modelling. In fact, as the specific heat of the M5 is less than that of Zy-4, the cladding temperatures will be increased. The characteristics used are reiterated below:
Thermal Temperature Density Specific heat Component Conductivity
[°C] [Kg.m-3] [J.kg-1.K-1]
[W.m-1.K-1]
20 200 UO2 pellet 400 10960 (constant) 600 800 20 200 M5 cladding 400 6500 (constant) 600 800 20 200 Helium (under 0.33 400 - -
pressure) (constant) 600 800 4.6 Boundary conditions The boundary condition of the model is a surface power equal to 145 kW/m², applied to the external surface of the cladding, and representing the flux emitted by the glycerine combustion in the vicinity of the cladding.
The power curve applied over the calculation duration of 10s is shown below:
Power (KW.m-2) 145 0
0 1 2 3 4 5 6 7 8 9 10 Time (s) 4.7 Initial temperature The initial temperature of the model is assumed to be 400°C, corresponding to the auto-ignition temperature of glycerine Non-proprietary version
TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 18 / 21 4.8 Results The maximum temperature of the cladding, reached after 1s, bounds that in Paragraph 3.1.3 after 0.3s of combustion, and is equal to °C.
4.9 Creep consequences The aim of this paragraph is to show that the localised heating of the claddings generates no significant distortions which might modify the behaviour of the rods during the fire test.
By assuming, in a highly conservative manner, that the totality of the glycerine is to be found within the thickness of one grid, and assuming a very low mass flow rate for glycerine, giving a combustion duration of 1 s, the maximum temperature of the claddings, calculated above, does exceed °C.
These temperatures correspond to a peak temperature relating to the combustion of the glycerine. As this peak lasts a very brief moment when compared to the regulatory fire duration, the cladding will heat, reaching a maximum temperature, and then resume the initial kinetics driven by the fire test.
Analysis of the creep in the rods involves calculating, using the temperature increase kinetics for the claddings, the circumferential stress within the cladding, which is compared with the instability criterion and the combination of the circumferential strains. The analysis is presented in Chapter 2.2-3 of the Safety Analysis Report.
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TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 19 / 21 The results for creep behaviour for the hottest rod are given below, respectively for cladding made of M5 and ZIRCALOY-4:
M5:
For the Rod 1 transient (hottest rod in the array) the minimum ratio of stress to instability criterion is 4.3. The overall circumferential strain reaches % while the maximum circumferential strain (hottest zone) reaches %. This level of strain is acceptable in that, for a temperature below 700°C, the measured minimum uniform strain is equal to around %.
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TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 20 / 21 ZIRCALOY-4:
For the Rod 1 transient (hottest rod in the array) the minimum ratio of stress to instability criterion is 3.4. The overall circumferential strain reaches % while the maximum circumferential strain (hottest zone) reaches %. This level of strain is acceptable in that, for a temperature below 700°C, the measured minimum uniform strain is equal to around %.
The above tables show that, for a temperature of less than 550°C, and for a duration of 100s, the contribution to overall strain and maximum local strain is in the order of 0.2%. As the duration of glycerine combustion is a maximum of 1s for a temperature of °C, the contribution to creep is negligible for M5 and Zy-4 claddings.
- 5. CONCLUSION Given the conservatisms included in this analysis, the presence of a residual 5 g of glycerine does not bring into question the mechanical behaviour of the rod claddings in the fuel assemblies.
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TN International Ref. DOS-13-00081778-205-NPV Rev. 0 Page 21 / 21
- 6. REFERENCES
<1> Bastos, Nilsson, et al., 1988, Thermodynamic properties of glycerol enthalpies of combustion and vaporization and the heat capacity at 298.15 K. Enthalpies of solution in water at 288.15, 298.15, and 308.15 K
<2> SSPE handbook of fire protection engineering- 4th edition.
<3> Introduction to Heat Transfer - Frank P. Incropera, David P. DeWitt - Third Edition.
<4> Characterization of Candle Flames, Journal of FIRE PROTECTION ENGINEERING, Vol. 15 - November 2005.
<5> Finite element calculation software: NX IDEAS 6.1 M1, distributed by SIEMENS PLM Software, linked to a TMG Thermal Analysis Module/Thermal flow 6.0.1181.
<6> MTDS - Glycerine Safety Data Sheet to Regulation (EC)
N° 1907/2006 (REACH) - Version 2 dated 8 August 2011 Non-proprietary version