L’analyse de structures par éléments finis : applications, innovations et défis

1. Mardi, 26 avril 2022 L’analyse de structures par éléments finis : applications, innovations et défis Tanguy Mertens, Product Manager Structure Solutions (Siemens) Jean-Philippe Ponthot, Professeur (Aérospatiale et Mécanique, ULiège)

2. LIEGE CREATIVE, en partenariat avec :

3. Welcome Where today meets tomorrow

4. Structural Design & Mechanical Integrity Mertens Tanguy 21st April 2022 Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow.

5. Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. Simcenter 3D The most comprehensive, fully-integrated CAE solution

6. What is Simcenter 3D? Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. Common engineering desktop Integrating multiple disciplines World-class solvers Simulating for engineering insight Data & Process Management Connecting simulation to development Integrated applications Achieving agile simulation processes

7. Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. Whole Engine Thermo-Mechanical (Structural Focus)

8. What Challenges Does A Gas Turbine Thermal & Structural Departments Face Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. How to create a correct 2D abstraction efficiently How to efficiently model all the missions What is the interplay between flow, thermal & structural phenomena? How to effectively collaborate How to interpret the results

9. Bolts Seals 3D geometry Cuts Projections Modifications How To Create A Correct 2D Abstraction Efficiently Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow.

10. How to efficiently model all the missions Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. A state Time definition Missions Trans-Atlantic + Refueling 50,000 ft July 4th A limited set of parameters drives the complete simulation

11. How To Effectively Collaborate Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. Modeling and validation on subsystem level Assembly thermo- mechanically bolted together Mission, boundary conditions inherited from subsystem

12. Predict Tip Clearance to Optimize Engine Performance Simcenter solutions Minimize clearance between blades and case to optimize engine performance Challenge 2D System Modeling Only way to model full engine system Thermal-Mechanical Coupling Include thermal and structural loads and their interactions Clearance Use expression to quickly compute clearance Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow.

13. Combined 3D Cyclic Symmetry and 2D Axisymmetric Simulation Simcenter solutions • Avoid excessive vibrations at typical engine operating frequencies (RPMs) • Predict engine life using high cycle fatigue methods Challenge Enable non-axisymmetric loads Enable multi-stage modeling of blades/disks Rather than performing individual blade/disk analyses in isolation Account for engine stages of different cyclic symmetry sector counts in the same model Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow.

14. Siemens Aero Engine Demo Model From a 3D CAD perspective Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. Engine Assembly Compressor Assembly

15. Siemens Aero Engine Demo Model From a 2D thermal-mechanical analysis perspective Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. 2D Engine Assembly

16. Siemens Aero Engine Demo Model From a 2D thermal-mechanical analysis perspective Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. 2D Engine Assembly Compressor rotor stages 3-6

17. Siemens Aero Engine Demo Model From a 2D-3D thermal-mechanical analysis perspective Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. 2D-3D compressor rotor stages 3-6 2D-3D Mesh

18. Siemens Aero Engine Demo Model From a 2D-3D thermal-mechanical analysis perspective Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. 2D-3D Mesh Meshing details • 3D solid cyclic symmetry sector • 2D axisymmetric solid • 2D plane stress with thickness

19. Siemens Aero Engine Demo Model From a 2D-3D thermal-mechanical analysis perspective Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. 2D-3D Mesh Multi-stage details • Analysis model stage 1: • 72 blades (cyclic symmetry sectors) • 5.000° sector angle • Analysis model stage 2: • 81 blades (cyclic symmetry sectors) • 4.444° sector angle • Analysis model stage 3: • 85 blades (plane stress blade thickness) • Analysis model stage 4: • 87 blades (plane stress thickness)

20. Simcenter Nastran Enabling Technology Cyclic symmetry support for 3D sector meshes Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. Cyclic symmetry details • Couple sector face pairs • Enforce consistent cylindrical displacements • Equivalent meshes on face pairs not required • Planar sector faces not required • Unequal sector angles for the stages permitted Stage 1 coupled faces Stage 2 coupled faces Engine Axis Engine Axis 11 sectors of both stages

21. Simcenter Nastran Enabling Technology 2D-3D coupling to enable multi-stage cyclic symmetry analyses Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. 2D-3D coupling details • Couple axisymmetric edges to equivalent 3D faces • Enforce consistent displacements at the 2D-3D interface • Equivalent / aligned 2D and 3D meshes not required • This coupling enables multi-stage cyclic symmetry modeling • Axisymmetric elements connect the engine stages Stage 1 coupled edge - face Stage 2 coupled edge - face

22. Siemens Aero Engine Demo Model Pre-stressed cyclic modes calculation Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. Simcenter Nastran multi-step nonlinear kinematics • SOL 402 is a multi-step, structural solution that supports a combination of subcase types (static linear, static nonlinear, nonlinear dynamic, preload, modal, Fourier, buckling and complex eigenvalues extraction) and large rotation kinematics. Solution Setup Loads Angular Velocity Temperature Glue / Contact

23. Combined Results from 2D and 3D regions 2D axisymmetric and 3D cyclic symmetry with multiple stages Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. Combined results • Cyclic mode 3 expansion of results Cyclic Index 0 294 Hz Cyclic Index 1 403 Hz Cyclic Index 2 1053 Hz Cyclic Index 3 1062 Hz Cyclic Index 4 1065 Hz

24. Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. Component Mechanical Integrity & Lifing

25. Process Amelioration Accurate cooling performance prediction Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. Cooling Flow Metal Temperature Structural Faster Engineering Insight Performance Synthesis Better Decisions Complex Geometry

26. Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. Simcenter solutions Engines are governed by physics of aerodynamics, thermal, and structural Need scalability to analyze for single physics or multiple physics. Challenge CFD Solution Thermal Solution Structural Solution Flow Definitions Stress and Deflections Cooling Flow Metal Temperature Structural Process Amelioration Multiphysics Component Simulation

27. Advanced Material Modeling Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. Simcenter solutions Aero-engine depend on high performance materials that operate in extreme conditions Need ability to accurately model nonlinear behavior of materials. Need ability to manage materials. Challenge Temperature Dependent Plasticity and Creep Materials Mulitilinear plasticity models with hardening High temperature creep materials User-Defined Link in proprietary advanced material models Damage Play failure and delamination models for composites Material Databases Links to commercial or in-house material databases

28. Advanced Material Modeling Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. Lifing analyzed on a long multistep mission combining rotational speed, high temperatures, pressures. Structure integrity depends advanced materials such as combined creep and plasticity Applied Force Unsymmetric Cyclic Load Unsymmetric Cyclic Load time Mission

29. Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow.

30. Blade Manufacture Hot-to-Cold Solution Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. Simcenter solutions Blade geometry is first defined for operating shape Operating shape is the manufactured shape + deformation from thermal and pressure loads How do you reverse engineer to get manufactured shape? Challenge Pressure and thermal loads mapped from CFD to structural “Unrun” structural solution for hot to cold – start with operating FEM shape and iterate to manufactured FEM shape Create new deformed geometry Operating Geometry (Hot) Manufactured Geometry (Cold)

31. Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow.

32. Dynamic Loading On Links For Strength And Fatigue Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow. Simcenter solutions Compressors are unstable at low speeds. Variable stator angles adjust air flow for speed changes and maintain stability and performance Challenge Stress Evaluation Ensure that stresses are acceptable for complete range of motion FE Kinematics FE model of blades with large rotation

33. Manufacturing and Assembly Simulation Simcenter solutions Aero-engines are assembled in stages with press fits and bolt tightening sequences. Need to understand the stress and deflections from the assembly process and include pre-stress effects with service loads Challenge Multistep Solutions • Add components in a series of steps • Sequence the actual tightening of bolts • Evaluate effect of bolt failure Initial Strain • Include residual stress/strain from manufacturing into components of an assembly Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow.

34. Bolted Assembly of Hub and Flanges Press Fit Flange 1 to Hub Bolts Tightened Bolt 2 and 3 Press Fit Flange 2 to Hub Rotating Service Load Bolts Tightened Bolt 1 and 4 Modes Service Loads Assembly Steps Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow.

35. Thank you. Unrestricted | © Siemens 2022 | Siemens Digital Industries Software | Where today meets tomorrow.

36. de structures par éléments finis : applications, innovations et défis Jean-Philippe PONTHOT, University of Liège, Belgium Romain Boman, Luc Papeleux Department of Aerospace and Mechanical Engineering JP.Ponthot@uliege.be M.L. Cerquaglia, B.J. Bobach, E.F. Sanchez-Fernandez, M. Lacroix, S. Février, C. Laruelle, Y. Crutzen, G. Tanaka Liège Creative, 26 avril 2022

37. Contents 2 1. Introduction/General context 2. Roll forming of complex parts 3. Wear/ Rotor Stator interactions in an aeroengine 4. Additive Manufacturing (macroscopic scale) 5. Alternative discretization techniques: PFEM

38. 3 J.-P. Ponthot Our lab within the university Numerical simulation Solid mechanics Fluid-Structure Interactions Finite element method Software development Computational Mechanics hydroforming of a tube Dept of Aerospace and Mechanical Engineering (Faculty of Applied Sciences)

39. Our main simulation code: Metafor 4 Implicit Finite-Element solver for the numerical simulation of large deformations of solids ALE Formalism, remeshing. Thermomechanical time-integration schemes. Modeling of cracks, fracture. Contact algorithms. Nonlinear constitutive laws. Mesh generation from medical images. Fluid finite elements. Monolithic schemes. Coupling with extenal solvers. Metal Forming applications Crash / Impact Biomechanics Fluid/structure interaction

40. pin shoulder welded zone advancing side retreating side Software development and numerical simulation of problems involving large strains, contacts, coupled thermo- mechanics and complex material behavior modeling: Metal forming processes (deep drawing and springback, superplastic forming, cold rolling, Impact simulation and crashworthiness Tire mechanics & rubber Biomechanics Research interests

41. 6 Industrial partners = owns a Metafor license

43. Roll forming 8 Industrial application Roll forming until the desired cross section is obtained Roll forming mill Process description

44. U-channel 9 Industrial application Roll forming Forming of a symmetrical U-channel Experimental mill (ArcelorMittal R&D, Montataire, France) 6 stands (15°, 32°, 50°, 68°, 80°, 90°) Final bending radii: 6 mm Inter-stand distance : 0.5 m Sheet : 2000 x 200 x 1.6 mm Sheet velocity: v = 200 mm/s Coulomb friction = 0.2 DP980 steel ( Y0 = 697.34 MPa) Numerical parameters Symmetry Friction drives the sheet Two layers of EAS elements Dynamic implicit scheme (Chung-Hulbert) Process parameters

45. U-channel 10 Industrial application Roll forming Numerical vs. experimental springback The final shape has been digitised using a high precision 3D measurement device and fits well both numerical curves (courtesy of ArcelorMittal) Lagrangian : (21 320 FEs) ALE : (12 768 FEs) CPU Times: ALE is 2.6x faster! DEFORMATION LONGITUDINALE J1 PEAU SUP EN FONCTION DE LA DISTANCE DE PROFILAGE -0,20% -0,10% 0,00% 0,10% 0,20% 0,30% 0,40% 9,00E+02 1,40E+03 1,90E+03 2,40E+03 2,90E+03 3,40E+03 3,90E+03 4,40E+03 4,90E+03 Distance de profilage en mm Déformation Ingénieur METAFOR MES. EXP.

46. Forming of a rocker panel 11 Industrial application Roll forming Simulation of an industrial line Process parameters 16 stands unsymmetrical shape Material: DP980 Sheet: 5950 x 165 x 1.5 mm Mesh 1 FE through the thickness FE length: from 3mm to 30mm 155 652 dofs stand #1 stand #16 forming direction closed cross section

47. Roll Forming of a Complex part 12

49. Recent Fan Blade Out Problem 14 Southwest WN1380 New-York-Dallas, April 17, 2018 Boeing 737-700/ CFM56-7B24 flying at 32 000 feet

50. Industrial application 15 Accidental buckling of blade in a low pressure compressor due to fan blade-out. Low pressure compressor Fan

51. Industrial application 16 Casing

52. Industrial application 17

53. Context and motivation Reduction of emissions and fuel consumption reduction in aero engines Contrails!

54. Context and motivation One way of increasing engine efficiency is to decrease the clearance between the rotating blades and the casing (thus avoiding leakage flows) A reduction of 25% of the clearance means an increase of 1% of the engine efficiency. Increasing by 1% engine efficiency leads to saving 200 000 liters of fuel per year for a middle range aircraft*! From the mechanical point of view, the clearance becomes so small that sometimes the blades come into contact with the casing (the shaft deforms during e.g. brutal manoeuvers or gusts To mitigate the contact forces, aircraft engine manufacturers use an abradable coating *Lattime S.B., Steinez B.M. Turbine Engine Clearance Control Systems: Current Practices and Future Directions. Report NASA/TM-2002-211794

55. Wear in Blade-Casing interaction 20 Abradable seal : Abradable Casing Blade Abradable thickness ~ 2-3 mm

56. Low Pressure Compressor = Booster Typical booster architecture Industrial partner: Safran Aero Boosters Yellow and red: rotating parts Blue: fixed parts Typical clearance: 2% blade chord e.g. 1mm for a 50 mm compressor blade

57. Typical abradable material The ideal abradables material must resist erosion (due to particle impacts but must be easily worn when hit by a blade. Typical abradables material (e.g. METCO 601NS, DURABRADE) Al-Si12% to resist erosion Polyester to allow abrasion by the blade Manufactured by thermal spray coating E ~ 1500 MPa

58. In case of contact the blades start to vibrate Worst case scenario: What is sometimes observed is a synchronization of the blade frequency with the engine configuration In other words the blade vibrates an integer number of times per revolution and interacts with the abradable (8 times per revolution in the figure on the right) Under some (unknown) conditions, the blade can start to vibrate with a large amplitude and hits the abradables several times during a revolution Two basic scenarios: The abradables is worn and there is no longer any interaction with the blades The self-excited process quickly leads to blade failure Blade tearing due to fatigue

59. A wear model for abradable materials We have to manage contact between the blade and casing, as well as wear of abradable material, while keeping computational time under control!

60. Wear update over a surface Wear surface is represented thanks to isoparametric coordinates . Wear profile is stored at the nodes (green dots), and can be interpolated. 3D Wear evolution algorithm in isoparametric space

61. Wear update over a surface The sponge-blackboard problem:

62. ONERA bench test 27 Bench test developed at ONERA/Centrale Lille, France, PhD of Sarah Baïz Etude expérimentale du contact aube/abradable : contribution à la caractérisation mécanique des matériaux abradables et de leur interaction dynamique sur banc rotatif avec une aube. N.B. Curvature is opposite to a aeroengine casing, but it allows a better view of the phenomenon VP = drum velocity DN & DT = Normal and tangential displacement FN = Normal Force T = strain at the base of the blade

63. ONERA Benchtest: fast camera imaging 28

64. ONERA Benchtest: numerical model 29

65. Numerical results Numerical results also exhibit 9 bounces

66. Comparison experimental /numerical

67. Comparison experimental /numerical 9 wear zones in each case ! Max wear experimental = ~65 µm Max wear numerical = ~70 µm

68. Experimental approach: Safran Aero Boosters Experimental set up: Thermal camera imaging during the test Wear pattern (8 lobes)

69. Experimental approach EO = Engine Order EO8 means 8 interactions per revolution (8 lobes ) Drawbacks of experimental approach: High cost! Low flexibility to test different blade designs Test rig availability Numerical model?

70. Parametric studies can be undertaken Typical wear pattern at different angular speeds (N is the number of lobes, T = torsional mode, F = Flexure/bending mode)

71. 8 lobes bending mode: experimental and numerical results

72. Wear pattern and gage signal evolution Wear pattern evolution Gage signal evolution N.B. The last two pictures show that the abradable has been broken in

73. Blisk model 56 blades One of the blades is a little bit longer A small mass (29 gr) to trigger unbalance Casing is not exactly centered! 12 926 hexahedral elements 67 776 Diameter =~500 mm

74. Full blisk model

76. Additive manufacturing test 3D (Metz) & collaboration with A-M Habraken (Uliège) 42 107 Layers (175mm) [2] ment Bourlet. Développement de la fabrication additive par procédé arc-fil pour les aciers : caractérisation microstructurale et mécanique des dépôts en nuances ER100 et 316L pour la validation des propriétés d'emploi de pièces industrielles. Autre [cond-mat.other]. Ecole nationale supérieure d'arts et métiers - ENSAM, 2019. Français. NNT : 2019ENAM0058 . tel-02860062

77. Additive manufacturing test 3D (Metz) 43

78. Experimental curves 44 Substrate temperatures (TKc5-8) :

79. Experimental curves 45 Temperatures in the wall (TKvr1-8): Interruption during building (not modeled)

80. Metafor model 46 Convection + Radiation TKvr1-8 TKc5-8

81. Metafor simulation 47 With remeshing: Taking all the cluster: 144 tests in ~18h Cluster No Remesh Remeshing CPU ( 12 Cores) ~1d15h ~7h30 CPU ( 1 core) ~3-4d ~18h No Remesh Remeshing Nelem 56724 56724 5634 Hanging nodes N/A 464

82. Experimental curves 48 Source: [2] Remark: All data was fit in time to the Metafor results on peak 3

83. Best parameters yet 49 Constant Substrate Conductivity 5.0 Deposit Material: Niccolini

84. Best parameters yet 50 Tkvr1 Constant Substrate Conductivity 5.0 Deposit Material: Niccolini

88. PFEM 54 New developments in PFEM Particle Finite Element Method

89. Motivation for PFEM 55 Avoid distortions such as those encountered in updated Lagrangian formulation for solid mechanics Combine the advantages of classical FEM and particle methods (e.g. SPH) at the nodes like in particle methods Evolution is computed thanks to a FEM discretization Use Lagrangian representation to easily track evolution of interfaces so there is no need for an interface tracking algorithm

90. PFEM: how does it work? 56 The first step in the PFEM is discretizing the continuum with some particles/nodes The particles carry all the physical and mathematical The equations are written in their Lagrangian form.Thus external boundaries are easily determined by following the particle motion.

91. At each time step a new mesh is quickly built and boundaries are determined thanks to the shape technique.This mesh is used to solve the weak form using classical FEM over one time step. Distorted elements and external boundaries are determined thanks to the shape algorithm Classical FEM computation

92. PFEM in the literature 58 Seminal contribution from E. Onate and S. Idelsohn: Idelsohn S.R., Oñate E., Del Pin F., The particle finite element method: a powerful tool to solve incompressible flows with free- surfaces and breaking waves, IJNME (2004) Oñate E, Idelsohn SR, Del Pin F, Aubry R. The particle finite element method. An overview. International Journal of Computational Methods 2004; 1(2):267 307. See e.g. Cremonesi et al., Arch. Of Comput. Methods in Eng. 2020, for a recent overview.

93. PFEM: Examples 59 Dam break Problem set Physical parameters Numerical parameters PSPG+Picard Pressure sensor location

94. PFEM: Examples 60 Dam break Results

95. Fluid-Structure Interactions 61

96. PFEM CUPyDO (Python) (C++) (C++) (C++) Implementation: coupling codes through Python Communications are performed through memory (No I/O files) No full execution of coupled codes No system calls SWIG: Simplified Wrapper and Interface Generator, http://www.swig.org 62 Multi-Physics/Multi-scale: coupling different codes

97. Examples 63 Geometrical parameters FSI parameters BGS Aitken relaxation Dam break against an elastic obstacle Problem set Solid properties Fluid properties

98. PFEM: Examples 64 Dam break against an elastic obstacle Results

99. Examples: FEM & PFEM coupling 65 Filling of an elastic container Problem set Geometrical parameters FSI parameters BGS Aitken relaxation IQN-ILS(30) Solid properties Fluid properties

100. Elastic container filling (PFEM & FEM coupling)

101. PFEM: Examples 67 Dam break against an elastic obstacle 3D Results

102. 3D results including contact 68

103. 3D results including contact 69

104. PFEM 70 Thermo-mechanically coupled PFEM with phase change

105. 71 Motivation: numerical simulation of weld pools multi-physics simulations at meso-scale Solid Liquid Solid Liquid Heat source (e.g. Laser LPBF, laser welding ) Heat source Heat transfer Melt pool fluid dynamics Melting & solidification Residual stresses and distortion after cooling transient & coupled unknown & evolving Interfaces

106. Equations to solve: Liquid, mushy & solid regions solved using same mesh using: Navier-Stokes equations (NSE) - Lagrangian form Heat equation 72 Latent heat absorption flow resistance of mushy zone (and solid) Surface tension/ Marangoni terms

107. Equations to solve Momentum equation for newtonian fluids Surface tension Resulting surface force term 73 Normal force Tangential Marangoni force Note: Marangoni coefficient usually negative surface force drives fluid away from heat source = curvature = outward normal = surface tension at = Marangoni coefficient Surface tension term

108. Surface tension example 74 Transition from a cube to a sphere Yellow arrows represent unit outward normals

109. Gallium melting Validate Latent heat solid flow resistance buoyancy Compare front evolution Sim. by Saldi (2012) Sim. by Brent et al. (1988) Exp. by Gau & Viskanta (1986) 75 (pure Gallium)

110. Gallium melting 76

114. Melting of a sample with moving laser 80 Laser heat flux: Laser position:

115. Equations to solve External heat source from laser 81

116. Melting of a sample with moving laser Temperature isocontours 82

117. 83 Melting of a sample with moving laser Blue: solid particle ( =0) Yellow: liquid particle ( =1)

118. 84 Fixed laser: generating a Keyhole Blue: solid particle ( =0) red: liquid particle ( =1)

119. Conclusions PFEM handles well free surface deformation Thermo-mechanical problems phase change with latent heat surface tension & Marangoni effect adaptive mesh refinement Fluid-Structure interactions Still a lot of work till realistic SLM (Selective on the way! 85

120. Conclusion 86 Conclusions Thank you for your attention! JP.Ponthot@uliege.be

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