STAR Global Conference 2014 - Vienna - 17 th -19 th March 2014 Forced Response Analysis of Radial Inflow Turbine using STAR-CCM+ Chair of Structural Mechanics and Vehicle Vibrational Technology Prof. Dr.-Ing. Arnold Kühhorn Dipl.-Ing. Frederik Popig Siemens-Halske-Ring 14, 03046 Cottbus, Germany Tel: (+49) 355 69-4853 Fax: (+49) 355 69-4805 E-mail: strukturmechanik@tu-cottbus.de
Content 2 Introduction 1 Forced response analysis 2 Prediction of modal forcing using STAR-CCM+ 3 Prediction of aerodynamic damping using STAR-CCM+ 4 Summary 5
Introduction 3 State of the art in radial inflow turbine design : blisk (blade integrated disk) 1 Advantage: Disadvantage : Increased efficiency Low mechanical damping 2 Sensitive to mistuning Tuned Modeshape Fundamental problems: 3 Low and high engine order excitation Mistuning 4 Modeling of Fluid-Structure-Interaction Identification of significant aerodynamic influences on the vibration behavior 5 Mistuned Modeshape Exact simulation of aerodynamic interaction essential Motivation: Accurate prediction of tuned blisk vibrations with low computational cost Determination of aeroelastic parameters via uncoupled approaches using STAR-CCM+
Forced Response Analyses – Basics 4 Modal transformed equation of motion: (1) ω 2 E q D q q f 1 m m ˆ ˆ E E f f 1 m, i η, m, i Modal frequency response function: (2) q V D 2 i ω m, i ω 2 2 η 2 2 2 η 2 (1 ) 4 D 0, i 0, i m, i ˆ E Ω f Maximum physical displacement : (3) m, i η φ φ 3 x q , 1(at resonance) i, max i, max i, max i, max ω ω 2 2 D m, i 0, i mod e depends on X max • Structural operating conditions 4 φ Modeshape: i Abaqus Eigenfrequency : f 5 i • Aerodynamic operating conditions ˆ E Modal excitation force : f m, i STAR-CCM+ Aerodynamic damping: D m, i Frequency response function How can we use STAR-CCM+ to estimate aerodynamic damping and forcing?
Forced Response Analyses – Process 5 Steady State CFD - Analysis Steady State CFD 1 p S (x,y,z) • Starting point: CFD-Solution after grid study T S (x,y,z) Setup configuration: 2 FEM φ i ,f i • Multi bladerow with mixing plane Unsteady State CFD • Reynolds-Averaged Navier Stokes Equations (RANS) 3 • Spalart-Allmaras Turbulence Model Aerodynamic Aerodynamic • Single passage rotor with periodic boundaries 4 Damping: Forcing: → Validation: comparison against measurement data of performance test 5 Torsional moment Isentropic efficiency
Forced Response Analyses – Process 6 Steady State CFD FEM-Analysis 1 p S (x,y,z) • Abaqus T S (x,y,z) 2 • Cyclic-symmetry model containing blade, disc and shaft sector FEM φ i ,f i • Application of rotational speed, pressure and temperature distributions Unsteady State CFD 3 Results: → Nodal diameter map Aerodynamic Aerodynamic → Modeshapes , Eigenfrequencies 4 φ f Damping: Forcing: i i BTW – Backward Travelling Wave FTW – Forward Travelling Wave 5 BTW FTW BTW FTW BTW FTW BTW FTW BTW FTW Nodal diameter map ND vs. EO diagram
Forced Response Analyses – Process 7 Steady State CFD Unsteady State CFD - Analysis 1 p S (x,y,z) • Starting point: Steady State CFD + FEM Solution T S (x,y,z) 2 • Requirements for application of unidirectional methods: FEM φ i ,f i Small vibration amplitudes Unsteady State CFD 3 Big blade mass ratio Aerodynamic Aerodynamic 4 Damping: Forcing: • Verification of aerodynamic interaction by modeling of the whole turbine system including 5 Volute Nozzle guide vane Radial inflow turbine Contourplot: Gradient of Density
Forced Response Analyses – Process 8 • Aerodynamic damping estimation for travelling wave modes 1 : Steady State CFD 1 p S (x,y,z) Determination of aeroelastic eigenvalues: T S (x,y,z) πn λ δ i ω 2 (5) (6) 2 FEM σ , ND n ND a, σ a, σ a, σ n n n n MAX MAX N ˆ φ i ,f i λ ω 2 N C a, σ σ σ ND , N even number of blades , 1 , 2 n n n MAX 2 Unsteady State CFD N 1 ND , N odd number of blades 3 MAX 2 δ λ σ (7) σ a, a, Re D n n σ a, ω λ n σ σ Aerodynamic Aerodynamic a, Im n n 4 Damping: Forcing: • Applicable unidirectional methods: A erodynamic I nfluence C oefficients Method ( AIC -Method) 1 5 - One simulation per blademode/operating condition - Partial or full assembly model - Applicable to harmonic balance or time-accurate solver H armonic B alance F lutter (HBF-Method) - One simulation per ND → (2·ND max +1) computations per blademode/operating condition - Single passage model, Phase-lag boundary conditions 1 [Crawley1987]
Forced Response Analyses – Process 9 Steady State CFD • Time history of modal excitation force for mode i: 1 p S (x,y,z) N T S (x,y,z) Cells (7) E T T φ n φ n f t p t dA p t A m, i i j i, j j j A 2 j 1 FEM φ i ,f i Unsteady State CFD 3 Aerodynamic Aerodynamic 4 Damping: Forcing: 5 Modal force timehistory • Discrete Fourier Transformation: πnk 2 N 1 1 i E k Δ f f t e N m, n m N k 0 Harmonic amplitudes of modal forcing
Modal forcing simulation - setup 10 Version: STAR-CCM+ 8.04.011 1 Configuration: • Implicit unsteady solver 2 • Mesh: STAR-CCM+ polyeder (14.4e6 cells) • Direct interface to ensure aerodynamic interaction 3 • Rigid rotor blades (non-vibrating) • Reynolds-Averaged Navier-Stokes Equations (RANS) 4 Model containing volute, nozzle guide vane and radial inflow turbine • Spalart-Allmaras Turbulence model • User defined library to store: 5 Unsteady pressure for each partition at each timestep Partitioning information of rotor blades • Validation of user defined functions: Comparison of unsteady torsional moment Comparison of unsteady torsional moment
Modal forcing simulation - setup 11 Example: Mode 6 / CSM 6 / E0 18 1 • Modeshape interpolation: Importing Abaqus result file 2 STAR-CCM+ surface mapping FEM - modeshape Interpolated modeshape • External fortran postprocessing routines for 3 Assembling pressure data Calculating modal forces 4 5 Modal sector force time history Harmonic amplitudes of modal forcing
Aerodynamic damping simulation - setup 12 Approach 1: AIC-method - unsteady time accurate solver 1 Example: Mode 1/ CSM 6 / EO18 • Model: Full-Assembly, reflecting inlet/exit boundaries 2 • Motion specification: morphing in rotating reference frame FE-Modeshape Interpolated Modeshape • Solver : Implicit unsteady 3 1 1 Δt , n number of timesteps per vibrationc ycle 150 Cycle Vibrating blade n f mode Cycle Rigid blades 4 • Coupled Flow model • Reynolds-Averaged Navier-Stokes Equations (RANS) 5 • Spalart-Allmaras Turbulence model • User defined field functions to calculate modal forces needed for calculation of AIC’s and damping CFD-Model
Aerodynamic damping simulation - setup 13 Blade 0:L 0 1 • Calculation of travelling wave mode coefficents ˆ S πin 2 f N 1 ˆ ˆ j σ (5) m, C n L e N σ ˆ i q n 2 i 0 • Calculation of aerodynamic influence coefficients 3 ˆ S f (6) L m, i i ˆ q i 4 5 Relative Aerodynamic Influence Coefficients Relative Modal Forces
Aerodynamic damping simulation - setup 14 Blade 0:L 0 Blade 1: L 1 1 • Calculation of travelling wave mode coefficents ˆ S πin 2 f N 1 ˆ ˆ j σ (5) m, C n L e N σ ˆ i q n 2 i 0 • Calculation of aerodynamic influence coefficients 3 ˆ S f (6) L m, i i ˆ q i 4 5 Relative Aerodynamic Influence Coefficients Relative Modal Forces
Aerodynamic damping simulation - setup 15 Blade 0:L 0 Blade 1: L 1 1 • Calculation of travelling wave mode coefficents Blade 2: L 2 ˆ S πin 2 f N 1 ˆ ˆ j σ (5) m, C n L e N σ ˆ i q n 2 i 0 • Calculation of aerodynamic influence coefficients 3 ˆ S f (6) L m, i i ˆ q i 4 5 Relative Aerodynamic Influence Coefficients Relative Modal Forces
Aerodynamic damping simulation - setup 16 Blade 0:L 0 Blade 1: L 1 1 • Calculation of travelling wave mode coefficents Blade -1:L N-1 Blade 2: L 2 ˆ S πin 2 f N 1 ˆ ˆ j σ (5) m, C n L e N σ ˆ i q n 2 i 0 • Calculation of aerodynamic influence coefficients 3 ˆ S f (6) L m, i i ˆ q i 4 5 Relative Aerodynamic Influence Coefficients Relative Modal Forces
Aerodynamic damping simulation - setup 17 Blade 0:L 0 Blade 1: L 1 1 • Calculation of travelling wave mode coefficents Blade -1:L N-1 Blade 2: L 2 ˆ S πin 2 f N 1 ˆ ˆ j Blade -2:L N-2 σ (5) m, C n L e N σ ˆ i q n 2 i 0 • Calculation of aerodynamic influence coefficients 3 ˆ S f (6) L m, i i ˆ q i 4 5 Relative Aerodynamic Influence Coefficients Relative Modal Forces
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