Fuel and Cladding Temperature in LFR ALFRED Test Case
Delve into the analysis of fuel and cladding temperature profiles in the ALFRED reactor during a test case in Trieste, Italy. Explore the thermal properties, axial power distribution, and core extrapolated height for a comprehensive understanding of this crucial aspect in nuclear reactor operation.
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Fuel and cladding temperature in LFR ALFRED test case Trieste, Italy, November 11st-15st, 2024 M. Tarantino, P. Cioli Puviani, A. Bellomo
Scope of the exercise Compute the temperature profile in the ALFRED reactor of: - lead (bulk) - cladding outer surface temperature - maximum fuel temperature Fuel and cladding temperature in LFR ALFRED test case
Schematic of the problem ??,? ??,? ????? ??,? ??,? ????? ??,? ????? ??,? ??,? ???? ????? ??,? ????? In steady state condition ?????= ????= ?????= ?????= ? 3 Fuel and cladding temperature in LFR ALFRED test case
ALFRED Fuel and FA Dummy element: d = 12 mm 4 Fuel and cladding temperature in LFR ALFRED test case
ALFRED data and hypothesis Data Data Power 300 MWth Cladding outside diameter 10.5 mm Power released in the Fuel Assemblies 95 % Cladding thickness 0.6 mm Gap cladding fuel 0.15 mm * Total mass flow rate 17174 kg/s Pitch to diameter ratio 1.29 Mass flow rate in the assemblies 98.5 % Fuel internal diameter 2 mm Hot channel factor 1.3 N Fuel assemblies 134 Fuel Assembly hexagonal key 156 mm Fuel rods per assemblies 126 + 1 Inlet temperature at the core 400 C Active length 810 mm Reactor cold and at the Beginning Of Life (BOL) * 5 Fuel and cladding temperature in LFR ALFRED test case
Lead Properties Quantity Formula Unit Thermal conductivity W / (m K) 9.2 + 0.011 ? 176.2 4.923 10 2 ? + 1.544 10 5 ?2 1.524 10^6 ? 2 Heat capacity J / (K kg) 4.55 10 4 exp(1069/?) Dynamic viscosity Pa s Density kg / m3 11441 1.2795 ? Temperature in Kelvin 6 Fuel and cladding temperature in LFR ALFRED test case
Axial power distribution in the hot channel The power at a given point depends on the position of the selected channel within the fuel assembly (FA), the position of the FA within the core, and the axial position. For define the power in the hottest channel the Hot Channel Factor (HCF) is defined as: ??? =??????? ?????? ????? ?? ? ? ?????? ? ????? ??????? ?????? ????? ?? ? ? ???? ? ? ??, where ??is the The axial distribution could be approximated by a cosine, cos Core extrapolated height. This concept helps model neutron flux distribution more accurately by accounting for the "leakage" effects at the core boundary, where neutrons do not abruptly drop to zero but instead gradually diminish. 7 Fuel and cladding temperature in LFR ALFRED test case
Axial power distribution in the hot channel ??= ???????+ 1.42 ? + 2? Core extrapolated height: ALFRED reactor saving: ? = 0.224 ? ALFRED mean free path: ? = 0.0378 ? It is the average distance travelled by a particle before it collides with another particle. It measures how efficiently neutrons are used to sustain the chain reaction. Depends on the neutronic properties of the core and the reflector. 8 Fuel and cladding temperature in LFR ALFRED test case
Power distribution Power Profile Power Profile Linear power axial distribution in the hot channel 3.50E+04 3.00E+04 ? ? ?? LINEAR POWER [W/m] 2.50E+04 ??? = ??,??? ??? 1.17cos 2.00E+04 1.50E+04 1.00E+04 Normalization factor Hot channel factor 5.00E+03 0.00E+00 40 81 0 122 162 203 243 284 ACTIVE LENGTH [mm] 324 365 405 446 486 527 567 608 648 689 729 770 810 9 Fuel and cladding temperature in LFR ALFRED test case
????? ? = ? (??,? ?????) Mikityuk correlation ????? ??,? ? ? 1 (??0.77+ 250) 3.8 ?? = 0.047 1 ? valid for 1.1 p/d 1.95 and 30 Pe 5000 Ushakov correlation 13 ?? = 7.55? ? ? + 0.041 ??0.756+1.19? ? 20 ? valid for 1.2 p/d 2 and 1 Pe 4000 10 Fuel and cladding temperature in LFR ALFRED test case
????? ? = ? ? ??? Not considered Axial conduction ?? ??,? ?316?= 9.248 + 0.01572 ? ??,? ??,? ? ??,? 2????? = ? ? ?? ??,? ??,? The result is a polynomial of the second order! 1 equation 1 unknown 11 Fuel and cladding temperature in LFR ALFRED test case
???? T Af,o(Tf,o Tc,i) ????= hg Contribution of radiation between surfaces. Depends on the ?4and the emissivity of the fuel and cladding. In this exercise this contribution is neglected. 12 Fuel and cladding temperature in LFR ALFRED test case
???? T Af,o(Tf,o Tc,i) ????= hg Contribution presents only if contact occurs. Neglected in this exercise. 13 Fuel and cladding temperature in LFR ALFRED test case
???? T Af,o(Tf,o Tc,i) The contribution due to the 3 thermal resistances in series is considered in this exercise ????= hg Computed with the Ross and Stoute correlation: next slide! Hp: the gap is in cold condition (no expansion of the fuel/cladding considered) and filled by only helium (BOL) at fixed pressure overall conservative assumption that reduce ??? 14 Fuel and cladding temperature in LFR ALFRED test case
???? Computed with the Ross and Stoute correlation: Helium thermal conductivity ???= 1.763 10 3 ?0.77163 ??? ???= ?2??+ ??? + ??+ ???+ ? Hp: ?2??+ ??? + ??+ ???= 2.5 10 5 ? where???is the gas thermal conductivity,? corresponds to the gap,?2is a roughness coefficient with??+ ???as the surface roughness, and ??+ ???are the temperature jump distance for the surrounding solid bodies. The gas temperature is computed as the arithmetic mean of the local temperatures of the surrounding surfaces. In the exercise ?2??+ ??? + ??+ ???is given. Hp: the gap is in cold condition (no expansion of the fuel/cladding considered) and filled by only helium (BOL) at fixed pressure overall conservative assumption that reduce ??? 15 Fuel and cladding temperature in LFR ALFRED test case
????? From energy conservation of the fuel with uniform volumetric heat generation Not considered Density variation in time Conductivity dependency from temperature and time ??,? 2 rf,o rf,? 2 ln ??,? ? ??,? ??? = 1 4? ??????? rf,? rf,? ??,? 1 ? ? ? Hp: ????? 2 16 Fuel and cladding temperature in LFR ALFRED test case
Mariano Tarantino mariano.tarantino@enea.it
