Dump Core ThermoMechanical Studies 4102017 XX Jaakko Johannes

Dump Core: Thermo-Mechanical Studies 4/10/2017 XX Jaakko Johannes Esala François-Xavier Nuiry Giulia Romagnoli Edouard Grenier Boley Jose Briz Monago Marco Calviani Vasilis Vlachoudis Tobias Polzin Yannick Coutron Didier Steyaert And all the involved people in EN-STI, EN-MME, EN-HE, TE-VSC, TE-MSC, BE-OP, BE-BI, BE-RF

Outline • Design History • Overview of thermo-mechanical simulations • Results • Steady-state • LHC 25 ns HL-LHC (Steady-state + 4 pulses) • Graphite results • Cu. Cr. Zr results • Other beam cases • Conclusions 4/10/2017 Dump Core: Thermo-Mechanical Studies 2

History • Maximum temperature in the front shaving edge Starting point: Current dump, but longer: 130 200 mm • Material: Oxygen Free Copper • Sensitivity to angle of the core Completely parallel dump impossible Angle set at 1° • Shaving process is a long (~ms) and local (~µm) process Thermal conductivity is a driving parameter 4/10/2017 200 mm BEAM Dump Core: Thermo-Mechanical Studies BEAM angle 3

Design History • m 200 m Edge rounded to spread out proton impacts and heat generation LANE P Y R T MME SY BEAM 22 % decrease • Rounded edge Location of temperature peak! 745 Other geometrical shapes and solutions also considered 15 ° mm “Sword” design: 35 % decrease in max. temperature compared to straight edge AM BE 4/10/2017 Dump Core: Thermo-Mechanical Studies 4

Material Selection MATERIAL SELECTION: • Thermal load case: Temperature increase thermal strain stress BEAM • Multi-turn, shaving impact makes thermal figure of merit difficult to assess: • Driving physical properties: ρ Density cp λ α E Specific heat Thermal conductivity Coefficient of thermal expansion Young’s Modulus Approach: 1) Material “sandwich”: 1) low density material with high temperature and thermal shock resistance 2) higher density absorbing materials 2) Good thermal conductivity 4/10/2017 Dump Core: Thermo-Mechanical Studies 5

Material Selection • Several material candidates evaluated: Graphite R 7550 Glassy Carbon Silicon Carbide Cu. Cr. Zr Copper Oxygen Free Glidcop AL-15 Copper Diamond Aluminum Ti 6 Al 4 V Molybdenum alloy TZM Tungsten alloy Inermet 180 • • • Low density Medium density High density Unacceptable temperatures and plastic deformations! Low density materials: • Graphite R 7550 • Silicon Carbide • Glassy Carbon 4/10/2017 Higher temperature in lower density materials! High elastic modulus (~400 GPa) high stresses. R 7550 better known. Low thermal conductivity ~7 W/(m K) Dump Core: Thermo-Mechanical Studies 6

Design History Medium density Low density High density HL-LHC Energy absorbed: 14. 5 k. J/pulse (16% of total) • • 10 mm of graphite not sufficient Unacceptable peak °C in Cu. Cr. Zr High steady-state temperatures Not enough space for sufficient dilution before dense materials Maximum length: 230 mm (due to vacuum tank dimensions) Cooling pipes away from particle showers 4/10/2017 Dump Core: Thermo-Mechanical Studies HL-LHC Energy absorbed: 8. 4 k. J/pulse (8. 7%) 7

ANSYS Model Overview 2 D layered shell elements: 30 layers x 5 µm = 150 µm 66 mm Slice 230 mm 40 mm s M BEA NE PLA Y R T ME SYM Rounded edge: 3 straight sections Rounded: 40 mm BEAM 120 mm 9. 5 23 24 mm Slices 10 mm 4/10/2017 23 Dump Core: Thermo-Mechanical Studies 8

Modeling Assumptions • Time stepping: 20 -60 x 150 µs (from FLUKA) • New Energy deposition map each time step • Vertical tune Q=6. 33 • Symmetry in geometry, loading and boundary conditions • Linear elastic temperature dependent material model • Dump core velocity: 0. 8 m/s • Beam impact always in the same position, in the middle 4/10/2017 Dump Core: Thermo-Mechanical Studies 9

Overview DESIGN CRITERIA: Limit Criteria Graphite Cu. Cr. Zr Method of evaluation Maximum temperature 2000 °C 300 °C ANSYS Simulations Failure criteria Mohr-Coulomb Von Mises yield ANSYS Simulations Material strength Tension: 40 MPa 1) Comp. : 130 MPa 1) 282 MPa 2) (at 22 °C) Fatigue Possible total beam dumps limitation Compare stress with S-N curves Mohr-Coulomb Safety Factor: σ1 is maximum principal stress (tensile) σ3 is minimum principal stress (compressive) ANSYS Help, Mohr-Coulomb Stress Safety Tool 4/10/2017 1) From manufacturer SGL Group, Material data sheets, and specific measurements for CERN 2) Cu. Cr. Zr Dump Core: Thermo-Mechanical Studies 3 D forged characterization at CERN (EN-MME), 2017 10

Sensitivity Studies • Sensitivity studies to validate the FEM model and assumptions: • FLUKA to ANSYS energy import, peak and total energy • Mesh convergence for graphite • Time stepping not influencing results Maximum temperature vs. dump core velocity LHC 25 ns HL-LHC beam, one pulse 1420 °C Mohr-Coulomb SF: 0. 99 • Beam impact location • Influence of dump angle and tune of the PS machine • Dump core velocity 1292 °C Mohr-Coulomb SF: 1. 21 98 °C 95 °C 4/10/2017 Dump Core: Thermo-Mechanical Studies 11

Boundary Conditions BEAM Thermal Contact Conductances [W/(m 2 K)] Contact Clamped HIP 2000 No contact Perfect thermal contact Cu. Cr. Zr - Cooling Pipe 2000 Perfect thermal contact Cooling Pipe - Water (at 26 °C) 6000 Graphite - Cu. Zr Cu. Cr. Zr Top – Cu. Cr. Zr Bottom 1) Upgrade of the PS Internal Dump in the Framework of the LHC Injectors Upgrade Project. EDMS No. 1845424 Rev. 0. 1 4/10/2017 Dump Core: Thermo-Mechanical Studies Calculated with Mikic equations: Corresponds to smooth surfaces, uniform contact pressure < 0. 05 MPa 1) Calculated with Mikic equations: Corresponds to smooth surfaces, uniform contact pressure of 0. 6 MPa 1) Analytically calculated value: 2800 W/(m 2 K) for a flow rate of 1. 5 l/min TCC = Thermal Contact Conductance HTC = Heat Transfer Coefficient 12

Steady-state, Clamped Design • Steady-state simulations are performed with averaged heating power. • The ~40 FLUKA time steps are summed and the energy is applied over the pulse period (3. 6 s for HL-LHC) • Power corresponding to a HL-LHC beam every 3. 6 seconds is used: 2400× 1010 protons/3. 6 s 667× 1010 protons/s 8323 joules/3. 6 s 2312 W Very conservative • Considered an reasonable upper limit after discussion with the operation group • TCC values and cooling performance calculated analytically are estimates. • Cooling performance shall be evaluated during prototyping and commissioning Simulations and power limits adjusted accordingly 4/10/2017 Dump Core: Thermo-Mechanical Studies 13

Steady-state, Clamped Design BEAM Graphite Max. T = 96 °C Clamped design Cu. Cr. Zr Max. T = 231 °C Thermal barrier Clamped: 96 °C HIP: 67 °C Clamped: 231 °C 29 °C 145°C HIP: 86 °C 4/10/2017 Dump Core: Thermo-Mechanical Studies 14

Steady-state, Clamped Design BEAM Baseline Temp = 96 °C Most sensitive thermal contacts: Cu. Cr. Zr - Cooling Pipe & Cooling Pipe - Water 4/10/2017 Dump Core: Thermo-Mechanical Studies Baseline Temp = 231 °C TCC = Thermal Contact Conductance HTC = Heat Transfer Coefficient 15

Steady-state, HIP Design New iteration: HIP design with precised boundary conditions Graphite – Cu. Cr. Zr TCC: 2000 1000 W/(m 2 K) 26°C Cooling Pipe - Water HTC: 6000 1000 W/(m 2 K) 48 °C Steady-state 4 pulses – HL-LHC Cu. Cr. Zr: 207 °C Graphite: 170 °C + Graphite: 1378 °C Cu. Cr. Zr: 267 °C For boundary condition calculations see: Upgrade of the PS Internal Dump in the Framework of the LHC Injectors Upgrade Project. EDMS No. 1845424 Rev. 0. 1 4/10/2017 Dump Core: Thermo-Mechanical Studies 16

Transient Thermal Results, HIP design Max. temp. in Cu. Cr. Zr Logarithmic! Initial beam impact point, Max. temp. in Graphite Beam LHC 25 ns HL-LHC Intensity 2. 4 × 1013 Momentum 26 Ge. V/c Size 3. 10 × 1. 45 mm×mm Pulse Steady-state + 4. pulse BEA M ~180 °C Water boiling temperature 170 °C at 8 bar Max. temperature in time 1378 °C Temperature along Z Path (at peak time) 1378 °C Graphite 210 °C 164 °C 4/10/2017 258 °C Cu. Cr. Zr Graphite Cu. Cr. Zr 258 °C Dump Core: Thermo-Mechanical Studies 17

Transient Structural Results, HIP design Exaggerated deformations! Beam LHC 25 ns HL-LHC Intensity 2. 4 × 1013 Momentum 26 Ge. V/c Size 3. 10 × 1. 45 mm×mm Pulse Steady-state + 4. pulse Max. strain rate ≈ 4 1/s (no elastic/plastic waves assumed) “No separation” boundary condition Deformation upward ~140 μm BEAM Unrealistic stresses due to rigid support 4/10/2017 Dump Core: Thermo-Mechanical Studies Thermal expansion Bending 18

Cu. Cr. Zr Structural Results, HIP design Cu. Cr. Zr at peak time Beam LHC 25 ns HL-LHC Intensity 2. 4 × 1013 Momentum 26 Ge. V/c Size 3. 10 × 1. 45 mm×mm Pulse Steady-state + 4. pulse Global maximum: 84 MPa BEA M v. Mises: 51 MPa 4/10/2017 Yield strength (300 °C) 230 MPa Representative stress 58 MPa Safety Factor 3. 96 v. Mises: 58 MPa Dump Core: Thermo-Mechanical Studies 19

Cu. Cr. Zr Conclusions and Fatigue • • Steady-state + 4 pulses Acceptable stresses in Cu. Cr. Zr Fatigue not expected to be critical for Cu. Cr. Zr Maximum temperature 258 °C (steady-state 207 °C) Max. representative von Mises stress 58 MPa Safety Factor Stress in Cu. Cr. Zr: 58 MPa (amplitude even lower) 3. 96 Maximum strain in Cu. Cr. Zr: 0. 04% 350 °C Low-cycle fatigue European Copper Institute. (2017) Cu. Cr 1 Zr Data Sheet, Retrieved from http: //www. conductivity-app. org/alloysheet/19 4/10/2017 G. Li, B. G. Thomas, J. F. Stubbins. (2000). Modeling Creep and Fatigue of Copper Alloys, Metallurgical and Materials Transactions A, pp. 2491 -2502. Vol. 31: 10 Dump Core: Thermo-Mechanical Studies 20

Cu. Cr. Zr Structural Results, HIP design Graphite at peak time X EAM -10 B Z Comp. strength 130 MPa Mohr-Coulomb SF 1. 17 6 M Pa Pa 1 M -11 150 µm 4/10/2017 40 MPa 1 mm 150 µm Stress evolution in Graphite in time Tensile strength Dump Core: Thermo-Mechanical Studies 1 mm 21

Graphite Block Studies Graphite block model: one pulse • Evaluate the effect of the slicing on graphite Beam HL-LHC • Studies with a smaller scale model with refined mesh Pulse no. One pulse Surface elements 3 D (instead of 2 D layered shells) 5 mm BEAM Initial beam impact point in the middle (highest heat generation). Slit depth: 5 mm 10 mm Fixed supports on the sides and on the bottom M BEA Thermal contact on the bottom: 2000 W/(m 2 K), ambient T=22 °C 4/10/2017 Dump Core: Thermo-Mechanical Studies 22

Graphite Block Studies Free surface = zero stress Temperature BEAM Stress due to thermal expansion (exaggerated) BEAM Y Stress Initial beam impact point 5 mm Z Stress 5 mm BEAM -90 MPa Sliced 4/10/2017 150 μm Tensile strength 40 MPa Comp. strength 130 MPa Mohr-Coulomb SF 1. 37 Dump Core: Thermo-Mechanical Studies 23

Graphite Block Studies X Path CONCLUSIONS: Z Path BEAM Y Path • Stress gradients follow temperatures gradients • Biaxial compression on the surface plane • Low stresses and temperatures outside the surface • Zero Y stress on the surface (free surface). • Low Y stresses in other parts due to thermal expansion 4/10/2017 Tensile strength 40 MPa Comp. strength 118 MPa Mohr-Coulomb SF 1. 37 Dump Core: Thermo-Mechanical Studies 24

Graphite Fatigue Preliminary analysis Determination of fatigue characteristics of NBG 18 graphite (molded) by Johan George Roberts 2007 4/10/2017 Fatigue failure and fracture mechanics of graphite for high temperature engineering testing reactor, Ishiyama et al, 1991. Dump Core: Thermo-Mechanical Studies 25

Graphite Conclusions Full model Block model (refined mesh) Steady-state + 4 pulses One Pulse 1378 °C (steady-state 170 °C) 1292 °C 1377 °C (+6. 6%) Max. stress X -106 MPa -102 MPa -94 MPa (-8%) Max. stress Z -111 MPa -107 MPa -90 MPa (-16%) 1. 17 1. 21 1. 37 (+13%) Pulses Maximum temperature Mohr-Coulomb Safety Factor CONCLUSIONS FOR GRAPHITE: • Peak temperature moderately affected by steady-state initial conditions BEAM • Stress gradients follow temperature gradients • Biaxial compression on graphite surface plane (otherwise low stresses) • Block model: Safety factor moderately improved • Graphite fatigue possibly limiting lifetime. Studies ongoing. 4/10/2017 Dump Core: Thermo-Mechanical Studies 5 mm Z Stress 26

Other Beam Scenarios • • Maximum temperature over time in Graphite Highest Int. most critical beam (with slicing safety factor >1) Highest Int. HL-LHC HL-BCMS and SFTPRO not critical HL-BCMS SFTPRO Simulations performed for the “clamped” design! With Graphite sliced block model Highest Int. : Safety Factor 1. 17 HL-LHC: Safety Factor 1. 37 4/10/2017 Dump Core: Thermo-Mechanical Studies 27

Conclusions • A dump core made of graphite and Cu. Cr. Zr is suitable for LIU beams. • 667 e 10 protons/second (2312 W) is the considered intensity rate limit for the HIP design. Further iterations of the cooling system will adjust the limit. • Cu. Cr. Zr shows reasonable safety factors with respect to HL-LHC beam. This is valid providing that the precipitation hardening following the HIP allows the recovery of thermal and mechanical properties. • Graphite fatigue seems to be a possible limitation. More actual beam dump statistics analysis are needed; Further graphite fatigue curves shall be studied. • Graphite safety factors are small, but the approach is conservative. 4/10/2017 Dump Core: Thermo-Mechanical Studies 28

Conclusions • Conservative assumptions in the simulations: • Rounded edge approximated with straight sections, leading to sharp peak temperature • Graphite compressive strength: Strength taken at room temperature. Graphite strength shows increase with temperature • Mohr-Coulomb safety factor is considered conservative for graphite • Graphite Young’s Modulus: Dynamic Young’s Modulus of 12. 8 GPa is used instead of static Young’s Modulus of 8. 5 GPa. • Tune Q=6. 33 used leads to higher temperature increase • Conservative steady-state case considered (667× 1010 protons/s) • Impact location always the same in the center 4/10/2017 Dump Core: Thermo-Mechanical Studies 29

Thank you 4/10/2017 Dump Core: Thermo-Mechanical Studies 30

Tune 4/10/2017 Dump Core: Thermo-Mechanical Studies 31

Angle 4/10/2017 Dump Core: Thermo-Mechanical Studies 32

Mesh 4/10/2017 Dump Core: Thermo-Mechanical Studies 33

Mesh details - “On the surface load case” Impact region modeled with 2 D layered shell elements coupled to 3 D elements Shell elements through-thickness thermal conduction 2 D shell elements (with layers) BEAM 3 D elements 4/10/2017 Energy from FLUKA is applied as element heat generation Temperatures TTOP 1 TE 10 2 TE 9 3 TE 8 4 TE 7 5 TE 6 6 TE 5 7 TE 4 8 TE 3 9 TE 2 10 TBOT Dump Core: Thermo-Mechanical Studies 5 µm 34

Materials • Temperature dependent material data implemented in ANSYS 4/10/2017 Dump Core: Thermo-Mechanical Studies 35

Time stepping • ANSYS HELP: Time step length should not be more than 100* • Too long time steps lead to numerically too high thermal conductivity • • • Approximate values for graphite: Lengthe = 5 e-6 m (5 micron) k = 100 W/(m K) c = 1000 J/(kg K) rho = 2000 kg/m^3 • Δt = 5 e-7 s = 0. 5 microsecond • Used time step: 1. 5 e-4 s (300 times Δt) • Smallest studied time step: 0. 5 e-4 s (100 times Δt) 4/10/2017 Dump Core: Thermo-Mechanical Studies 36

Stress waves • No elastic or plastic stress waves assumed • Smooth temperature increase during dumping • Maximum strain rate: 4 1/s Bertarelli, A. in Proceedings of the Joint International Accelerator School: Beam Loss and Accelerator Protection, Newport Beach, United States, 5– 14 November 2014, edited by R. Schmidt, CERN-2016 -002 (CERN, Geneva, 2016), pp. 159 – 227, http: //dx. doi. org/10. 5170/CERN-2016 -002. 159 J. Zazula. From Particle Cascade Simulations (FLUKA) to Finite Element Heat Transfer and Structural Deformation Analyses (ANSYS). Presented at the 2 nd Workshop on Simulating Accelerator Radiation Environment, CERN, Geneva (October 9 -11, 1995) 4/10/2017 Dump Core: Thermo-Mechanical Studies 37

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Highest Int. results • Highest Int. beam more critical than HL-LHC With Graphite Block submodel HL-LHC: 1377 °C Highest Int. : 1656 °C With Graphite Block submodel HL-LHC: 1. 37 Highest Int. : 1. 17 Intensity interlock for dumping of the Highest Int. can be specified in accordance with the functional specification 4/10/2017 Dump Core: Thermo-Mechanical Studies Simulations performed for the “clamped” design! 39

Graphite Block 4/10/2017 Dump Core: Thermo-Mechanical Studies 40

Energy import 4/10/2017 Dump Core: Thermo-Mechanical Studies 41

Irradiation damage in Cu. Cr. Zr • dpa in the order of 0. 002 dpa per year (0. 04 dpa in 20 years) (from FLUKA) • Localized peak dpa on the surface • Information for neutron irradiation found in literature. • Cu. Cr. Zr shows radiation hardening until saturation values around 0. 1 – 0. 5 dpa. [1][3] Some hardening may occur • Cu. Cr. Zr is void swelling resistant [1][2] (below 2% density change for dpa up to 150 [1]) • [3] [2] [1] Some thermal conductivity degradation may occur (5 – 10 % reduction for doses > 0. 1 dpa at < 150 °C [2]) [1] C. Bobeldijk (ed. ). (1994). Atomic and Plasma-Material Interaction Data for Fusion. Vol. 5. Supplement to the Journal Nuclear Fusion [2] S. A. Fabritsiev & S. J. Zinkle & B. N. Singh. (1996). Evaluation of copper alloys for fusion reactor divertor and first wall components. Journal of Nuclear Materials. Vol. 233 -237. pp. 127 -137. [3] M. Li & M. A. Sokolov & S. J. Zinkle. (2009). Tensile and fracture toughness properties of neutron-irradiated Cu. Cr. Zr. Journal of Nuclear Materials. Vol. 393. pp. 36 -46. 4/10/2017 Dump Core: Thermo-Mechanical Studies 42