COMSOL and ANSYS crosscheck Edvard Stubberud TEMPEPE 10182021

COMSOL and ANSYS crosscheck Edvard Stubberud, TE-MPE-PE 10/18/2021 Document reference 1

Motivation • Crosscheck with FEM based tool (ANSYS with user -defined elements) Implemented equations • • • Quench behavior Material property fits Coupling of physics Automated tests for Continuous Integration • • Consistency of models when developing Standard pattern for further incremental development 10/18/2021 Document reference 2

Test setup • Incremental steps Minimal physics Simplified geometry Constant material properties New features for new test • • • Automatic workflow Automatic test setup Create model with SIGMA • • • Geometry and cable parameters Set up simulation parameters Execution Post process • • Set up simulation Execute simulation Initialization • Create model Extract appropriate variables Compare with reference (and ANSYS) 10/18/2021 Extract results Compare Document reference 3

List of all test • Test 0, Geometry • • Test 1, Electromagnetic • • Temperature, Ohmic heat, Coil resistance Test 3, Material Fit • • • Magnetization from IFCC and ISCC, Heating from IFCC and ISCC Test 2, Thermal • • Magnetic flux in coil, Flux and differential inductance, B-field Copper resistivity – Tau IFCC, Resistivity of copper and homogenized cable Heat Capacity – Heat capacity of copper, G 10, Nb 3 Sn and homogenized cable Test 4, Circuit coupling • Dump resistor in series with magnet Simulation Active IFCC/ parameters physics ISCC Ohmic Forced Quench loses quench off Test 0 EM No No Test 1 EM Yes No No No Test 2 EM, TH No Yes No Test 3. A EM No No Test 3. B TH No No Test 4. A EM No No Test 4. B EM Yes No No No Test 4. C EM No No Yes No Test 4. D EM, TH Yes No No Yes Test 4. E EM, TH Yes No No No For detailed setup see: 10/18/2021 Document reference 4

Test 1 A, Electromagnetic, IFCC Create model Simulation Active IFCC/ parameters physics ISCC Ohmic Forced Quench loses quench off Test 1 No EM Yes No No Set up simulation Execute simulation Extract results Material properties • External stimulus Active physics Time interval (0, 1 e-3) [s] Current interval (0, 1) [A] Time step 20 e-6[s] Compare 10/18/2021 Document reference 5

Test 1 A, Electromagnetic, IFCC Q_iffc_HT 0 M_ifcc_x 1, 40 E-04 7, 00 E+00 1, 20 E-04 6, 00 E+00 1, 00 E-04 Q_iff_HT 0 [W] M_ifcc_x [A/m] 8, 00 E+00 5, 00 E+00 4, 00 E+00 3, 00 E+00 2, 00 E+00 8, 00 E-05 6, 00 E-05 4, 00 E-05 2, 00 E-05 1, 00 E+00 0, 00 E+00 2, 00 E-04 4, 00 E-04 6, 00 E-04 8, 00 E-04 1, 00 E-03 1, 20 E-03 Time [s] COMSOL ANSYS 10/18/2021 COMSOL ANSYS Document reference 6

Summary COMSOL crosschecked with ANSYS • All test fully automated • Easy scalability of all test • 10/18/2021 Document reference 7

Model setup T 0 Insulation Thickness insulation radial [m] 100 e-6 Thickness insulation azimutal [m] 100 e-6 [m] 50 e-6 Diameter strand [m] 0. 75 e-3 Twist-pitch strand [m] 0. 1 Fraction Copper [-] 0. 6 Fraction Nb 3 Sn [-] 0. 4 RRR [-] 100 T reference for RRR [K] 295 T operational [K] 1. 9 Cross contact resistance [Ohm] 16. 3 e-6 Adjacent resistance [Ohm] 10 e-6 effective resistivity [-] 1 Twist-pitch filament [m] 10 e-3 Width [m] 15 e-3 Height internal [m] 1. 5 e-3 Height external [m] 1. 5 e-3 Number of strands [-] 40 Number of strands per layer [-] 20 Number of layers [-] 2 Degradation [-] 0 Copper resistivity [Ohm∙m] (1/π)e-8 critical current [A] 50 e 3 Filament Diameter filament Strand Transient Cable Other 10/18/2021 Calculated cable time constants Tau IFCC tau ISCC crossover tau ISCC adjacent wide tau ISCC adjacent narrow [s] [s] Iron ρ k Cv [Ωm] [W/m/K] [W/m 3/K] 0 - Glass fiber ρ k Cv [Ωm] [W/m/K] [J/m 3/K] 0 0. 01 750 Nb 3 Sn ρ k Cv [Ω m] [W/m/K] [J/m 3/K] 0 300 250 Copper ρ k Cv [Ωm] [W/m/K] [J/m 3/K] 1 e-8/pi 300 500 1 e-3 1 (40π/3)e-3 (π/2)e-4 Document reference 9