PREPARATION OF HEXCALIBER TESTS AND PRELIMINARY THERMO-MECHANICAL ANALYSES I. Ricapito a, G. Dell Orco b, P. A. Di Maio c, R. Giammusso c, A. Malavasi a, A. Tincani a, G. Vella c a ENEA C.R. Brasimone (BO), ITALY b EFDA CSU Garching bei Munchen, GERMANY c DIN University of Palermo (PA), ITALY
OUTLINE TEST CAMPAIGN OBJECTIVES EXPERIMENTAL PART: Mock-up description Mock-up instrumentation and assembly Activity Schedule Time THERMO-MECHANICAL MODELLING: Model description Model preliminary results CONCLUSIONS
TEST CAMPAIGN OBJECTIVES
TEST CAMPAIGN OBJECTIVES (1/2) In the frame of EU Fusion Technology Programme, promoted by EFDA, ENEA FIS-ING at CR Brasimone is performing activities on thermo-mechanical characterisation of HCPB blanket mock-ups by an integrated experimental and theoretical approach. Experimental approach Theoretical approach Experiments on HELICA (done) and HEXCALIBER (to be done) mock-ups Analysis and correlation of the experimental data by a FEM code (ABAQUS) ad hoc implemented (del. TW5-TTBB-001-D6)
TEST CAMPAIGN OBJECTIVES (2/2) Aim of the test campaign on HEXCALIBER (He-Fus3 EXperimental CAssette of LIthium BERyllium Pebble Beds) is to provide, like in HELICA I-II, experimental results for the thermomechanical modelling BENCHMARK EXERCISE. As a consequence, the fact that HEXCALIBER is quite far from the present HCPB-TBM design is not a significant issue. HEXCALIBER will be tested in He-Fus3 facility at ENEA CR Brasimone under operative suitable to reproduce a TBM relevant thermal field in pebble beds
EXPERIMENTAL PART
MOCK-UP DESCRIPTION (1/3) HEXCALIBER essentially consists of two OSi pebble beds and two Be pebble beds each of them heated both heated by two flat electrical heaters. 254 mm 250 mm 540 mm The overall poloidal height, the toroidal width and radial depth of mock-up box are respectively 250 mm, 540 mm and 254 mm
MOCK-UP DESCRIPTION (2/3) OSi beds Be beds first wall back view The first wall is simulated by a flat plate with rectangular channels while five radial-toroidal martensitic steel cooling plates separate the OSi and the beryllium pebble beds
MOCK-UP DESCRIPTION (3/3) LATERAL CROSS VIEW n. 2 heaters per pebble bed
MOCK-UP INSTRUMENTATION AND ASSEMBLY (1/7) PARAMETERS to be measured/controlled Wall-to-wall bed temperature profile; He coolant I/O temperatures; He coolant pressure; He coolant flow rate; He purge pressure; He purge flows rate; heater power supplies; cup spring load displacement by LVDT
MOCK-UP INSTRUMENTATION AND ASSEMBLY (2/7) The temperatures distributions will be measured by 52 T/Cs located at 3 different toroidal positions : - 9 for each beds - 2 on the heaters surfaces Hexcaliber will be filled with: HEATERS - T/Cs SUPPORTING FRAME - 6 kg of SCHOTT Li 4 SiO 4 pebbles with diameter 0.2-0.4 mm; - 11 kg of NGK (Japan) Be pebbles with diameter 1 mm; both materials characterized by FZK Both Be and ceramic Li beds will be packed by with pneumatic hammering
MOCK-UP INSTRUMENTATION AND ASSEMBLY (3/7) TCs position in OSi bed 2.7 10 2.7
MOCK-UP INSTRUMENTATION AND ASSEMBLY (4/7) TCs position in Be bed 9.65 23.7 8.30
MOCK-UP INSTRUMENTATION AND ASSEMBLY (5/7) CASSETTE ASSEMBLY Lithiate ceramic beds Beryllium beds
MOCK-UP INSTRUMENTATION AND ASSEMBLY (6/7) HEXCALIBER BERYLLIUM RESISTOR
MOCK-UP INSTRUMENTATION AND ASSEMBLY (7/7) HEXCALIBER FINAL ASSEMBLY FRONT VIEW
ACTIVITY SCHEDULE TIME glove box adaptation and report on safe operation of the experimental set-up: mid October Be and OSI pebbles filling: end of October Test campaign: concluded for the end of December 2006
THERMO-MECHANICAL MODELLING
Model Description At Department of Nuclear Engineering of the University of Palermo (DIN) a theoretical constitutive model has been developed under the fundamental hypothesis that pebble beds can be treated as continuous, homogeneous and isotropic media characterised by effective properties depending on their thermal, stress and strain conditions; The functional expressions of these properties have been assessed either by means of purposely-outlined semi-theoretical procedures or by iteratively reproducing the results of the typical tests performed on pebble beds by EU Associations (oedometric, biaxial and triaxial tests).
Model Description THE THERMAL MODEL The thermal constitutive model is subdivided into two sub-models, accordingly to the different thermal behaviours observed within the bed bulk region or at the interface with the containing walls. The bulk region is modelled with an uniform and isotropic tensor of thermal conductivity that has been assumed to depend on local temperature and mechanical volumetric deformation as follows: mech mech ( εvol ) 0 ( α βεvol ) kt, = k 1+ T+ I The interface region is modelled as a thermal gap whose conductance can be derived to depend on pressure and temperature as follows: 3 k g 2k 1 p C = + 2 s 1 f π μn 1 1 2 n N
Model Description THE DIN MECHANICAL MODEL The mechanical constitutive model is subdivided into the following sub-models. Non-linear elasticity model. It has been developed under the fundamental hypothesis that pebble bed logarithmic bulk modulus depends more than linearly on pressure and provides a deformation modulus given by: 31 ( 2ν ) p E( p) = k0 ( )( ) ( ) 1+ μ ( ) 1 + μ ln 1 α + β p α + β p0 + + β 1 e0 1 μ Plasticity model. The Drucker-Prager Modified with Cap model and the Gurson model have been adopted to simulate the irreversible behaviour of fusion pebble beds. They are already implemented in the ABAQUS code and their effective parameters for a given fusion pebble bed have been determined by a semi-theoretical procedure based on the results of proper oedometric tests. The Gurson model is at the present preferred since it reduces numerical convergence problems.
Model Description The oedometric tests have been used in correlative way to provide the main constitutive model parameters. Then ABAQUS FEM, with the constitutive, model has been used to predict the biaxial tests, then giving a first validation of the model. 6 5 Numerical prediction Polydisperse Li 4 SiO 4 pebble bed 6 5 Numerical prediction σ (ε) [MPa] 4 3 2 σ(ε) [MPa] 4 3 2 1 1 0 0.0E+00 3.0E-03 6.0E-03 9.0E-03 1.2E-02 1.5E-02 1.8E-02 ε Drucker- Prager/Cap Vertical pressure σ v [MPa] 6 5 4 3 2 1 0 Experimental Numerical prediction 0.0 0.5 1.0 1.5 2.0 2.5 u x /H [%] σ h =0.012 Mpa 2 h Pressione verticale [MPa] 6 5 4 3 2 1 0 0 Experimental 0 0.004 0.008 0.012 0.016 ε Numerical prediction σ h = 0.012 MPa 2 h 0.0 0.5 1.0 1.5 2.0 2.5 u x /H [%] Gurson
Model Description THE HEXCALIBER THERMO-MECHANICAL PRELIMINARY ANALYSES Within the framework of the benchmark exercise launched by EFDA, DIN has just concluded a preliminary analysis to predict the HEXCALIBER thermo-mechanical performances under typical steady state conditions. As coupled analyses revealed to be "dramatically" time consuming and provided that pebble bed thermal and mechanical constitutive models are strictly coupled, it has been decided to carry out iteratively uncoupled thermal and mechanical analyses. Next iteration NO T i (x,y,z)-t i+1 (x,y,z) < Δ lim YES END i th thermal analysis T i (x,y,z) T i+1 (x,y,z) (i+1) th thermal analysis i th mechanical analysis σ i (x,y,z) ε i (x,y,z) p i (x,y,z) k i (T, ε(x,y,z)) C i (T, p(x,y,z))
Model Preliminary Results THE HEXCALIBER THERMO-MECHANICAL PRELIMINARY ANALYSES The FEM model A 3D finite element model of HEXCALIBER mock-up has been set-up simulating a slice, 1 cm thick, of the whole mock-up. It is composed of 78987 nodes and 49320 (D)C3D8 brick elements.
Model Preliminary Results The FEM model Cooling channels Forced convection with He (300-400 C) Pressure = 8 MPa Electric heat generation within Heating Plates q ( r,t) = ρ ( T) J( r) 2 Natural convection with air Thermal contact model at the interface bed-wall and bed-heater. No sliding allowed at the interface Plain strain assumed in the vertical direction
Model Preliminary Results The thermal field The thermal field shows typical parabolic profiles within each bed. Maximum temperature of Li 4 SiO 4 pebble bed = 819 C Maximum temperature of Be pebble bed = 563 C
Model Preliminary Results The results The equivalent volumetric strain field in Li 4 SiO 4 pebble beds The equivalent volumetric strain field indicates a compressive strain state for the whole pebble bed. Maximum volumetric strain reached is 0.17 mech ε vol
Model Preliminary Results The results The equivalent volumetric strain field in Beryllium pebble beds The equivalent volumetric strain field indicates again a compressive strain state for the whole pebble bed. Maximum volumetric strain reached is 0.16 mech ε vol
CONCLUSIONS Hexcaliber mock-up, consisting of two OSi and two Be pebble beds, is ready to be installed and tested in He-Fus 3 loop. The experimental campaign is planned to be concluded at the end of 2006 Although not compliant with the latest HCPB-TBM design, Hexcaliber has been designed and instrumented in order to provide input data to continue the benchmark exercise with different FEM codes, extending to Be beds the work so far done on the basis of the experimental data coming from Helica. In the FEM developed by DIN (based on ABAQUS) the thermal and mechanical analysis are uncoupled. The preliminary FEM results on Hexcaliber appear realistically consistent with those found in the previous Helica experimental campaign.