Influence of abradable coating wear mechanical properties on rotor stator interaction A. Batailly, M. Legrand, C. Pierre Structural Dynamics and Vibration Laboratory – McGill University
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Outline 1 Introduction 2 Structural model 3 Contact dynamics 4 Abradable coating modeling 5 Results 6 Conclusion and perspectives A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 2 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Industrial context combustion chamber compressor booster fan • Modern turbomachines • Optimization of power efficiency • ⇒ new designs (higher casing conicity, clearance closure...) A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 3 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Industrial context • Compressor stage • Possible parasitic leakage • ⇒ significant loss of power A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 3 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Industrial context CASING BLADE • Compressor stage • Possible parasitic leakage • ⇒ significant loss of power A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 3 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Industrial context • Modeling of abradable coating ◮ Mono-dimensional plastic law ◮ Plastic finite-elements around the casing • Blade / abradable coating contact simulations ◮ Variation of the material parameters of the abradable coating ◮ Consequences over the blade’s amplitude of vibration ◮ Consequences in terms of wear level A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 3 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Outline 1 Introduction 2 Structural model 3 Contact dynamics 4 Abradable coating modeling 5 Results 6 Conclusion and perspectives A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 4 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Blade • Industrial finite element model ( ≃ 65 , 000 dof) • 8 nodes used for contact management between the contact nodes leading edge and the trailing edge f Ω • clamped boundary conditions between the blade and the disk • use of the Craig-Bampton CMS (ROM contains 85 dof) e r e z f Ω clamped e θ boundaries Both centrifugal stiffening and � Blade with eight interface nodes clearance closure are taken into account A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 5 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Blade 35 • ROM of 85 dof • Good approximation of the 8 28 first eigenfrequencies over the frequency 21 rotational frequency range 14 7 0 0 0.1 0.2 0.3 0.4 rotational frequency � Campbell diagram of the ROM A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 5 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Outline 1 Introduction 2 Structural model 3 Contact dynamics 4 Abradable coating modeling 5 Results 6 Conclusion and perspectives A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 6 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Contact dynamics • Master/slave approach (abradable/blade), • Contact forces computed from plastic deformation of the abradable element, • Kuhn and Tucker contact conditions: ∀ x ∈ Γ m c (master surface) t N � 0 , g ( x ) � 0 , t N g ( x ) = 0 ◮ t N discretized contact pressure ◮ g gap function A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 7 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Contact dynamics Algorithm: • Master/slave approach 1. prediction of the displacements (abradable/blade), without considering abradable coating, • Contact forces computed from plastic deformation of the 2. determination of the gap abradable element, function g , • Kuhn and Tucker contact 3. abradable internal forces conditions: ∀ x ∈ Γ m c (master computation through a surface) deformation increment ∆ ε t N � 0 , g ( x ) � 0 , t N g ( x ) = 0 introduced by predicted displacements, ◮ t N discretized contact pressure 4. displacements correction compatible with the calculated ◮ g gap function contact forces. A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 7 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Outline 1 Introduction 2 Structural model 3 Contact dynamics 4 Abradable coating modeling 5 Results 6 Conclusion and perspectives A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 8 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Theoretical description • one-dimensional two-node bar elements casing • nonlinear plastic constitutive law abradable e r profile θ • numerical profile in order to represent blade width e θ rotation blade tip bar element • casing is assumed perfectly � Blade interface node numerical profile rigid A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 9 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Theoretical description • one-dimensional two-node bar elements casing • nonlinear plastic constitutive law abradable F c e r θ profile θ • numerical profile in order to F c F c represent blade width e θ r rotation blade tip bar element • casing is assumed perfectly � Blade interface node numerical profile rigid One layer of abradable elements per contact node on the blade tip ⇒ ≃ 16.000 abradable elements on the casing A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 9 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Theoretical description Plastic constitutive law σ • Young’s modulus E K σ Y • Plastic modulus K • Yield limit σ Y E ε ε p � Plastic law for abradable modeling A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 9 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Case study • Blade-tip/casing abradable interaction, • One blade (disk dynamics is neglected in this example), • Imperfections of the casing: deformed casing deformation along 2 and disk 5-nodal diameter free vibration modes, f Ω • Simulation parameters abradable coating (normalized) ◮ E = 11 ◮ K = 0 . 5 � Casing shapes for case study ◮ σ Y = 1 . 5 · 10 − 8 ◮ f Ω ∈ [0; 0 . 4] ◮ θ = 0 A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 10 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Case study f Ω dependent wear level map 2 π • Abradable profiles at the end of each simulation pictured 3 angular position (rad) with colour code, 2 wear • Distinct wear profiles with π both odd and even number of lobes, 1 • Two critical velocities 0 0 appear. 0 . 24 0 . 32 0 . 4 0 . 08 0 . 16 f Ω � Abradable coating wear patterns A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 10 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Case study s e s s s e b e e f Ω dependent wear level map b o b b l o o o 0 l l l 1 5 6 4 2 π • Abradable profiles at the end 1 of each simulation pictured 3 angular position (rad) with colour code, 2 2 wear • Distinct wear profiles with 3 π both odd and even number 4 of lobes, 1 5 • Two critical velocities 0 0 appear. 0 . 24 0 . 32 0 . 4 0 . 08 0 . 16 f Ω � Abradable coating wear patterns Complementary results: blade response spectrum for f Ω ∈ [0; 0 . 4] A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 10 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Case study eo ( k = 5) eo ( k = 4) C 1 � Spectrum of the blade response A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 11 / 19
Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives Case study eo (6) eo (4) � Spectrum of the blade response A. Batailly, M. Legrand, C. Pierre Turbo Expo 2011 June 9 2011 11 / 19
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