رسالة ماجستير بعنوان Suppression of Vibratory Stresses in Turbine Structural Components Subjected to Aerodynamic Loading

رسالة ماجستير بعنوان Suppression of Vibratory Stresses in Turbine Structural Components Subjected to Aerodynamic Loading
اسم المؤلف
Imran Aziz
التاريخ
18 مايو 2022
المشاهدات
323
التقييم
(لا توجد تقييمات)
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رسالة ماجستير بعنوان
Suppression of Vibratory Stresses in Turbine Structural Components Subjected to Aerodynamic Loading
Author
Imran Aziz
2010-NUST-MsPhD-Mech-08
Supervisor
Imran Akhtar
Department of Mechanical Engineering
College of Electrical & Mechanical Engineering
National University of Sciences and Technology
Islamabad
Table of Contents

  1. CHAPTER 1 .14
    1.1 Background, Scope and Motivation .14
    1.1.1 Fluid Dynamics and Rotor Stator Interaction 15
    1.1.2 Forced response .16
    1.1.3 Computational Methods .20
    1.1.4 Single Passage Modeling .23
    1.1.5 Material Damping 25
    1.2 Thesis Overview 28
    1.3 Thesis Objectives .30
  2. CHAPTER 2 .32
    2.1 Navier Stokes Equations 33
    2.2 Turbulence .33
    2.3 Turbulence Modeling .35
    2.3.1 Turbulence Modeling .35
    2.3.2 The Zonal SST Model by Menter 36
    2.4 Transition .38
    2.5 Discretization and Solution Theory 39
    2.5.1 Numerical Discretization .39
    2.5.2 Discretization of the Governing Equations 39
    2.5.3 Order of Accuracy .42
    2.5.4 Shape Functions .42
    2.5.5 Control Volume Gradients .43
    2.5.6 Advection Term .44
    2.5.7 High Resolution Scheme .44
    2.5.8 Diffusion Terms .44
    2.5.9 Pressure Gradient Term .45
    2.5.10 Compressibility .45
    2.5.11 Transient Term 46
    2.6 Interface Modeling .47
    2.7 Transient Blade Row Modeling Theory .47
    2.7.1 Time Transformation Method 49
    2.8 Dynamic Analysis 51
    2.8.1 Solution of the Equation of Motion .54
    2.8.2 Free Vibration Analysis .54
    2.9 Damping Types 55
    2.10 Forced Vibration Analysis .57
    2.11 Direct Frequency Response Analysis .609
    2.12 Modal Frequency Response Analysis 61
    2.13 Energy Dissipation Method of Damping due to Coating .63
  3. CHAPTER 3 .65
    3.1 Geometry Detail and Distinct Features 65
    3.2 Meshing Details .67
    3.3 Boundary Conditions .70
    3.4 Simulation Methodology 71
    3.5 Grid Independence Study .71
    3.6 Results and Discussions .74
    3.6.1 Comparison: Steady State, Profile Scaling, Time Transformation 86
    3.6.2 Time Averaged Unsteady Flow Calculations 88
    3.7 Computation of Aerodynamic Loads .96
  4. CHAPTER 4 .99
    4.1 Technique for Finite Element Modeling 99
    4.2 Preprocessing .101
    4.3 Analysis 103
    4.3.1 Uncoated Beam Free Vibration Analysis .103
    4.3.2 Coated Beam Modal Analysis .105
    4.3.3 Frequency Response Analysis of Uncoated Beams .106
    4.3.4 Coated Beam Frequency Response Analysis .107
    4.4 Curved Blade Analysis .109
  5. CHAPTER 5 .115
    5.1 Frequency Response Analysis under Concentrated Force .120
    5.2 Frequency Response Analysis under Steady State Aerodynamic Loading 124
    5.3 Effect of Changing the Orientation of Coating on Damping Performance of Magnetomechanical Coating
    126
  6. CHAPTER 6 .131
  7. APPENDIX A .134
  8. REFERENCES
    List of Figures
    Figure 1.1: Collar Triangle of Aero elasticity (Left), Forced Response analysis principle (right) .17
    Figure 1.2: Campbell Diagram [12] 18
    Figure 1.3: Summary of the analysis procedure for axial turbine blade .29
    Figure 2.1: Control Volume Discretization 40
    Figure 2.2: Interpolation Points in an element 41
    Figure 2.3: One passage periodicity cannot be applied 48
    Figure 2.4: Workaround using Standard Periodicity 48
    Figure 2.5: Phase Shifted Periodic Boundary Conditions 49
    Figure 2.6:Dynamic Process Environment .52
    Figure 2.7: Harmonic Forced Response without damping [85] 58
    Figure 2.8: Harmonic Force Response with Damping [85] .60
    Figure 3.1: Axial Turbine Geometry details [90] .66
    Figure 3.2: O-H Block Topology along with generated Mesh .68
    Figure 3.3: Blade to Blade view of Mesh at 50% Span 69
    Figure 3.4:Grid Independence of pressure envelops at mid span .73
    Figure 3.5:Position of the plane 1 (first stator exit), plane 2 (rotor) and plane 3 (second stator exit) 74
    Figure 3.6: Turbulence Kinetic Energy at the exit of stator 1, rotor and stator 2. 75
    Figure 3.7: Mach number Contour at the first stator1, rotor and stator 2 exit 75
    Figure 3.8: Absolute flow angle at the first 1, rotor and stator 2 exit .75
    Figure 3.9:Pressure Contours at the hub and rotor wall in rotor domain. .76
    Figure 3.10: Static Entropy at the stator 1, rotor and stator 2 exit 76
    Figure 3.11: Vector plot of Vortices at first stator exit .77
    Figure 3.12: Vector plot of Vortices at rotor exit .77
    Figure 3.13: Vector plot of Vortices at stator 2 exit .78
    Figure 3.14: Entropy contours in streamwise direction along the rotor blade 79
    Figure 3.15:Mach number contours in stream-wise direction along the rotor blade 79
    Figure 3.16: Contours of turbulence kinetic energy in streamwise direction along the rotor blade. 80
    Figure 3.17: Time Transformation Method, Entropy Contours at 10 %, 50 %, 90 % Span .81
    Figure 3.18: Time Transformation Method, Entropy Contours at the exit of stator 1, rotor and stator 2. 81
    Figure 3.19:Profile Scaling Method, Blade to Blade unsteady Entropy contours (25%, 50%, 75%, and 100%) Pitch
    distance 82
    Figure 3.20: Blade to Blade Mach number Contours (25%, 50%, 75%, 100% pitch) 83
    Figure 3.21: Profile scaling method, Instantaneous entropy contours behind rotor (25%, 50%, 75%, and 100%)
    Pitch .83
    Figure 3.22:Instantaneous entropy contours behind second stator (25%, 50, 75%, 100) Pitch 8411
    Figure 3.23: Boundary layer capturing at pressure and suction side of the blade .84
    Figure 3.24: Vortex Core Region, Full three dimensional Views. .85
    Figure 3.25: Streamlines from Stator 1 inlet to stator 2 outlet 85
    Figure 3.26: Prediction of Tip Clearance, Secondary and Horse Shoe Vortices 86
    Figure 3.27:Comparison between steady and unsteady entropy contours from Inlet to outlet at10% and 50% span,
    First row shows steady contours, second row shows unsteady contours. 86
    Figure 3.28:Comparison Entropy Span wise entropy contours, Steady State, Profile Scaling, Time Transformation
    at the exit of first stator 88
    Figure 3.29: Comparison Entropy Span wise entropy contours, Steady State, Profile Scaling, Time Transformation
    at the exit of rotor blade .88
    Figure 3.30:Comparison Entropy Span wise entropy contours, Steady State, Profile Scaling, Time Transformation
    at the exit of second stator. 88
    Figure 3.31: Mach number convergence (a) at inlet of vane-1. (b) at the outlet of vane-2 89
    Figure 3.32: Comparison of total pressure (absolute) at the exit of vane 1. .90
    Figure 3.33: Comparison flow angle (absolute) at the exit of the vane-1 .90
    Figure 3.34: Comparison of total pressure (absolute) behind the trailing edge of the rotor. 91
    Figure 3.35: Comparison of flow angle (absolute), behind the trailing edge of the rotor .91
    Figure 3.36: Comparison of total pressure (absolute), behind the trailing edge of the vane-2. 92
    Figure 3.37: Comparison of flow angle (absolute), behind the trailing edge of the vane-2 92
    Figure 3.38: (a) Predicted contours of total pressure behind the trailing edge of the first vane. (b): Predicted
    streamlines on suction side of the blade 94
    Figure 3.39: Comparison of unsteady pressure envelopes at mid-span 95
    Figure 3.40: Aerodynamic forces in X, Y and Z direction on blade suction surface 96
    Figure 3.41: Aerodynamic forces in X, Y and Z direction on blade pressure surface 96
    Figure 4.1: Beam Geometry and Meshing 102
    Figure 4.2: Mode shapes for first four bending modes of an uncoated beam .104
    Figure 4.3:Mode shapes for first four bending modes of coated beam .105
    Figure 4.4:Von Mises stress and displacements for uncoated beam for third bending mode .106
    Figure 4.5: Displacement and von Mises stress for First mode of uncoated Beam 107
    Figure 4.6: Displacement and von Mises stress for Second mode of uncoated Beam 107
    Figure 4.7: Displacement and von Mises stress for third bending mode of coated Beam 108
    Figure 4.8: Comparison Chart showing % stress and displacement reduction (y axis) vs. First 3 modes (x axis) in
    rectangular cantilevered beam .109
    Figure 4.9: Original Blade (7” x 3” x 0.34”) 109
    Figure 4.10: Curved Plateμ (7” x 3” x 0.35”) 110
    Figure 4.11: Isometric view of the meshed blade. 110
    Figure 4.12: Third and fourth stripe modal displacements of the coated cantilevered blade 11212
    Figure 4.13: The von Mises stresses in second stripe mode of the uncoated and coated turbine blade 113
    Figure 4.14: The von Mises stresses in third stripe mode of the uncoated and coated turbine blade .113
    Figure 4.15: The von Mises stresses in fourth stripe mode of the uncoated and coated turbine blade .113
    Figure 4.16: Stress reduction vs. mode number 114
    Figure 5.1:(a) Turbine structural components orientation with respect to each other (b) Mapping of fluid dynamic
    loads on structural nodes. 116
    Figure 5.2: The von Mises stress in first mode of uncoated and coated axial turbine blade .117
    Figure 5.3: The von Mises stress in second mode of uncoated and coated axial turbine blade 118
    Figure 5.4: The von Mises stress in first stripe mode of uncoated and coated axial turbine blade .118
    Figure 5.5: The von Mises stress in second stripe mode of uncoated and coated axial turbine blade. .119
    Figure 5.6: von Mises stress (Ksi) comparison between uncoated and coated blade .120
    Figure 5.7: von Mises stress (Ksi) comparison between uncoated and coated blade .121
    Figure 5.8: von Mises stress in the 2nd and 3rd bending mode of the coated blade under concentrated force .122
    Figure 5.9: Vibratory stress comparison in the coated blade due to aerodynamic and concentrated loading .123
    Figure 5.10: % Stress reduction comparison between aerodynamic and concentrated loading 123
    Figure 5.11: Displacement and Stress distribution in turbine blade for first mode under steady state aerodynamic
    loading .124
    Figure 5.12: Displacement and Stress distribution in turbine blade for second mode under steady state aerodynamic
    loading .125
    Figure 5.13: Displacement and Stress distribution in turbine blade for first stripe mode under steady state
    aerodynamic loading 125
    Figure 5.14: Displacement and Stress distribution in turbine blade for second stripe mode under steady state
    aerodynamic loading 126
    Figure 5.15: View of Magnetomechanical Coating on the top and bottom surface of the blade 127
    Figure 5.16: Displacement and Stress distribution in turbine blade with coating on top surface for first mode 127
    Figure 5.17: Displacement and Stress distribution in turbine blade with coating on top surface for second mode 128
    Figure 5.18: Displacement and Stress distribution in turbine blade with coating on top surface for first stripe mode.
    .128
    Figure 5.19:Displacement and Stress distribution in turbine blade with coating on top surface for second stripe
    mode. .129
    Figure 5.20:Stress reduction comparison between the pressure side and suction side coating .13013
    List of Tables
    Table 3-1: Geometrical Data of IST Turbine [90] 66
    Table 3-2: Aachen turbine Geometrical Parameters 66
    Table 3-3: Grid Points for Each Domain 70
    Table 3-4: Boundary Conditions Assumed for CFD Analysis 70
    Table3-5:Meshes for Grid Independence 72
    Table 3-6: Flow Parameters at the Vane-1 inlet .97
    Table 3-7: Flow Parameters at the Vane-1exit 97
    Table 3-8: Flow Parameters at the rotor blade inlet 97
    Table 3-9: Flow Parameters at the rotor blade exit .97
    Table 3-10: Flow Parameters at the Vane-2 inlet .98
    Table 3-11: Flow Parameters at the Vane-2 exit .98
    Table 4-1: Mechanical Properties of Substrate Materials .101
    Table 4-2: Mechanical Properties of Substrate Materials .101
    Table 4-3: Summary for Uncoated Beam Modeling .102
    Table 4-4: Steps for Coated Beam Modeling 103
    Table 4-5: Natural Frequencies of first four bending modes of uncoated beam .104
    Table 4-6: Natural Frequencies of first four bending modes of a coated beam 105
    Table 4-7: Stress and Displacement Reduction % for first three bending modes. 108
    Table 4-8:Natural Frequencies for uncoated and coated blade .111
    Table 4-9: Maximum stress (Ksi) comparison of Cantilevered Blade 112
    Table 5-1: Natural frequency of uncoated and coated turbine blades .117
    Table 5-2: Maximum stress comparison of uncoated (Ksi) and coated axial turbine blade (Ksi) under aerodynamic
    loading .119
    Table 5-3: Maximum stress comparison of uncoated (Ksi) and coated axial turbine blade (Ksi) under concentrated
    harmonic loading .121
    Table 5-4: Vibratory Stress Comparison (Ksi) between Steady and Unsteady Loading 126
    Table 5-5: Von Mises Stress Distribution in top coated axial turbine blade .129

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