Thermomechanical Simulations of the PS Internal Dump Francois-Xavier Nuiry Giulia Romagnoli Tobias Polzin

Agenda Material Choices From Energies to Mechanical Stresses Results

Increase of energy density per temperature increase Material Choices Various alloys available (2000 different metal alloys in CES Selector) For evaluation of different alloys a performance factor was defined. It consists of the thermal robustness in combination with the ability to absorb energy with a low temperature increase. This factor should be has high as possible. Increase of energy density per temperature increase

Considered factors: Material performance factor Material Choices Considered factors: Material performance factor Availability of material and material data Machinability RP requirements (activation) vacuum requirements (outgassing)

Material Choices Sorted with performance factor Titanium Alloys Ti12Mo6Zr2Fe Grade21 R58210 (Ti15Mo3Al3Nb0.2Si) Ti6Al4V Grade 4 Nickel Alloys EP741NP Rene 41 UDIMET 500 Nimonic 81 Nimonic 90 Nichrome 70/30 UDIMET 700 Nimonic 80A Hastelloy S Inconel 718 Haynes 230 Nimonic 75 Inconel 625 Inconel 600 Tungsten Alloys INERMET 180 Tungsten-25Rhenium Sorted with performance factor

Sliced core reduces the axial stresses Material Choices Resulting Geometry Beam direction Ti6Al4V Rene41 Sliced core reduces the axial stresses

From Particles to Mechanical Stresses ANSYS thermal Import of energy distribution and application as internal heat generation Beam parameters FLUKA Monte Carlo Simulation of particle interactions ANSYS mechanical Import of temperature distribution and application as load Energy distribution Temperature distribution

FE model construction Quality Assurance for Simulation Setup Model geometry represents reality Material models are valid for load case (temperature dependency, …) Material data clearly referenced FLUKA import to ANSYS carefully cross-checked Mesh quality studied and mesh convergence achieved Assumptions for simulation setup (timing, damping) are not influencing the result

Thermal Results ACCIDENTAL LHC25 SFTPRO ACCIDENTAL SCENARIO 26 GeV 5×1013 σ = 1.8 mm x 4.7 mm Pulse time 2.1 µs Pulse period 2.4 s 3 consecutive pulses LHC 25ns BEAM 26 GeV 2.3×1013 σ = 1 mm x 4.7 mm Pulse time 2.1 µs Pulse period 3.6 s 5 consecutive pulses then cooling down time of 20 s STFPRO BEAM 14 GeV 2×1013 σ = 2 mm x 3.7 mm Pulse time 2.1 µs Pulse period 1.2 s 2 consecutive pulses then cooldown time of 15 s ACCIDENTAL LHC25 SFTPRO Average heating power over pulse period / kW - 2.5 1.0 Material Ti6Al4V Rene 41 Maximum Temperature over maximum number of continous pulses spec. in EDMS 1582110 / ⁰C 185 260 132 178 72 64 MST* / ⁰C 350 877 *Source: GRANTA, CES Selector 2015

Thermal Results ACCIDENTAL scenario: 5E13 p+ @ 26 GeV/c in 2.1E-6s after third impact 185⁰C 260⁰C

Results LHC25ns scenario: 2.4E13 p+ @ 26 GeV/c in 2.1E-6s Thermal after fifth impact 132⁰C 178⁰C Before next cycle 56⁰C 83⁰C Still 83⁰C in the Rene 41 without cooling

Results SFTPRO scenario: 2E13 p+ @ 14 GeV/c in 2.1E-6s Thermal After second impact 72⁰C 64⁰C Before next cycle 34⁰C 31⁰C Still 34⁰C in the Rene 41 without cooling

ACCIDENTAL after third impact Results Mechanical – Eq. v. Mises Stress ACCIDENTAL after third impact 122 MPa 445 MPa ACCIDENTAL scenario occurs about 1500 times over lifetime  no fatigue calculation Ti6Al4V Rene41 Eq. v Mises Stress / MPa 122 445 Yield Strength / MPa 880 (at 200⁰C) 827 (at 370⁰C) Safety Factor 7.2 1.8 Source: Metallic Materials and Elements for Aerospace Vehicle Structures, Military Handbook - MIL-HDBK-5J Department of defense, Federal Aviation Administration, 2003

Results Mechanical – Eq. v. Mises Stress LHC25 after fifth impact Ti6Al4V Rene41 Eq. v Mises Stress / MPa 73 253 Yield Strength / MPa 950 (at 132⁰C) 825 (at 204⁰C) Safety Factor 13 3.2 Source: Metallic Materials and Elements for Aerospace Vehicle Structures, Military Handbook - MIL-HDBK-5J Department of defense, Federal Aviation Administration, 2003 Appears frequently (expected about 3 million times over lifetime), fatigue is studied. Maximum v. Mises Stress occurs in the second block of Rene 41 after five continuous impacts

Results Mechanical – Fatigue studies To evaluate the fatigue of the materials, isothermal fatigue tests are considered as source for the fatigue strengths. The load cycles are assumed to happen all at the maximum temperature For Ti6Al4V the stresses stay always under the fatigue limit of 300 MPa (3E6 cycles with stress ratio=0 at 480⁰C, unnotched specimen, solution treated and aged)* Rene41 needs closer fatigue investigation *Source: Metallic Materials and Elements for Aerospace Vehicle Structures, Military Handbook - MIL-HDBK-5J Department of defense, Federal Aviation Administration, 2003

Fatigue curves for Rene 41 at 371⁰C Fatigue curve for Rene 41 Fatigue curves for Rene 41 at 371⁰C STILL STUDIED!!!! 200 MPa (220 MPa at RT) 530 MPa (582 MPa at RT) 3 million cycles Source: FATIGUE OF RENE 41 UNDER CONSTANT AND RANDOM-AMPLITUDE LOADING AT ROOM AND ELEVATED TEMPERATURES, NASA Technical Note TN D-3075

Pressure in second Rene41 block after first LHC25 impact Results Mechanical Two dominant stress states in the cores: Internal stresses in the core caused by concentrated heat in the center (compressive stresses in the center surrounded by tensile stresses) Reflections of mechanical waves at the surface in the center of each core after each impact (high tensile stress peaks) Pressure in second Rene41 block after first LHC25 impact

Results Mechanical – Fatigue Studies Stress state on Surface of second Block of Rene41 Normal Stress in x-Direction Normal Stress in z-Direction Normal Stress in y-Direction The Material in the surface is able to deform in axial direction  plane stress

Each value is lower than 530MPa for a lifetime of 3E6 cycles Results Mechanical – Fatigue Studies Stress state on Surface of second Block of Rene41 The maximum stress intensity (TRESCA) is 157 Mpa. The maximum von Mises eq. stress is 140 Mpa. The maximum principle stress is 156 Mpa. Each value is lower than 530MPa for a lifetime of 3E6 cycles Source: FATIGUE OF RENE 41 UNDER CONSTANT AND RANDOM-AMPLITUDE LOADING AT ROOM AND ELEVATED TEMPERATURES, NASA Technical Note TN D-3075

Each value is lower than 530MPa for a lifetime of 3E6 cycles, Results Mechanical – Fatigue Studies Stress state in Center of second Block of Rene41 The maximum stress intensity (TRESCA) is 261 Mpa. The maximum von Mises eq. stress is 252 Mpa. The maximum principle stress is 122 Mpa. Each value is lower than 530MPa for a lifetime of 3E6 cycles, Source: FATIGUE OF RENE 41 UNDER CONSTANT AND RANDOM-AMPLITUDE LOADING AT ROOM AND ELEVATED TEMPERATURES, NASA Technical Note TN D-3075

Results Mechanical – Fatigue Studies Stress state in the second Block of Rene41 The stress state in the center is complex The fatigue data is received in a different load case The data looks promising but has to be closer checked v. Mises eq. Stress

Following Post-Processing Reviewing the fatigue data of Rene41, including radiation damage Evaluation of the Stresses in the Ti6Al4V housing Evaluation of the Stresses in the brazed surfaces Stresses during long term use with an implemented cooling system, so far there is no steady state considered

Material Choices Combination of materials necessary Increasing density to absorb gradually more energy Titanium as first material seems feasible Tungsten as last material may be possible Preliminary studies done by W. Kozlowska Combination of three materials Nickel alloy seems promising in between Follow up by D. Morgan Source: “LHC Injectors Upgrade: Technical Design Report – Volume 1 – Protons” (EDMS:1451384/4) “Preliminary Thermo-Mechanical Simulations Applied to the New PS Internal Dump” (EDMS:1539643)

From Particles to Mechanical Stresses FLUKA Based on chemical composition and density a deposed energy distribution is calculated via FLUKA (Thanks to ES-STI-FDA) The energy is then assumed to be focused in the center of the bin

From Particles to Mechanical Stresses Quality Assurance for Import ACCIDENTAL LHC25 SFTPRO FLUKA ANSYS Error Maximum of deposed Energy / J/cm3/pulse 321 317.0 1.2% 176 178.06 1.0% 80 79 1.3% Overall deposed Energy / kJ/pulse 40.7 39.1 4.0% 18.75 18.27 3.0% 8.3 8.1 2.4%

From Energies to Mechanical Stresses Used Material Properties density sp. heat therm. conduct. CTE Young’s mod. poiss. ratio Kg/m3 J/kg/C W/m/C 1E-6/C GPa Temperature region / C 20-750 20-700 20-500 20-430 Ti6Al4V 4430 - 4331 557 824 7.23 12.93 8.75 10.3 116 84 0.31 Rene 41 8250 280 694 10 17.26 12 14.4 189 147 0.29 Source: Metallic Materials and Elements for Aerospace Vehicle Structures, Military Handbook - MIL-HDBK-5J Department of defense, Federal Aviation Administration, 2003

From Energies to Mechanical Stresses Geometric Simulation Model Symmetry (geometry and boundary conditions) Symmetry planes

From Energies to Mechanical Stresses Meshing Bonded Contact Side view Characteristics of the full model mesh Number of Elements 248k Kemax/Kemin 1.2E3 Average skewness (standard deviation) 0.76 (0.13) Front view

From Energies to Mechanical Stresses Mesh Size horizontal coarse vertical fine

From Energies to Mechanical Stresses Mesh Size: Submodelling needed for one core of each material Finer meshing for the core with the highest stresses per material. Mesh size 0.3 x 0.3 x 0.5 mm Mesh characteristics with submodelled core for Rene 41 Number of Elements 128k Kemax/Kemin 2.2E10 Average skewness (standard deviation) 0.06 (0.13) Beam Beam

From Energies to Mechanical Stresses Simulation Setup (timing) Thermal conduction takes place in a larger time scale than the load application Division of each pulse in three loadsteps (duration): First step is to apply the beam energy (few microseconds) Second step is for simulating mechanical waves (100 microseconds) Third step allows to apply the temperature distribution corresponding to the end of the pulse period (0.01 seconds)

Backup Temperature distribution is calculated in a discrete way. For each time step in the thermal simulation there is a Temperature field. These fields have to be applied in the mechanical simulation at a fixed time step . In general the next mechanical time to apply the load is defined by In the first two load steps per pulse the mechanical and the thermal time steps are equal so we say: For the last load step we define for the mechanical time step

From Energies to Mechanical Stresses Maximum temperature Thermal simulation time Start of next impact Maximum temperature Mechanical simulation time Start of next impact after 0.01s

From Energies to Mechanical Stresses Simulation Setup (damping) For faster convergence damping is necessary Also more realistic, because each material has natural damping After 1E-4s there is no peak in the stresses expected (observed in past STI experience) After this time, damping should take effect. Assumption: a conservative damping ratio is selected: Eigen frequencies taken from FFT With Rayleigh damping we damp in the stiffness matrix with 1E-8

Fatigue Data for Rene41 For the Rene 41 there is one source for the fatigue strength, even for random loading. The data was received by bending of a thin notched probe The notch is designed to cause a stress intensity factor of around 7 Source: FATIGUE OF RENE 41 UNDER CONSTANT AND RANDOM-AMPLITUDE LOADING AT ROOM AND ELEVATED TEMPERATURES, NASA Technical Note TN D-3075

Fatigue Data for Rene41 Stress is calculated for a bar with the width of the notched region To get the fatigue strength for a unnotched part, this stress has to be corrected The stress intensity factor is only valid for a stress over the bigger width

Fatigue Data for Rene41

Backup Explaining that scaling to 0.01s is possible