1

CFD Open Series

Revision 1.85

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Essentials of Turbo
machinery in CFD
Ideen Sadrehaghighi, Ph.D.

Flow in Axial
turboMacines (CD-
Adapco)

Unsteady Flow
in Axial
TurboMachines
(ANSYS)

Unsteady Flow in
Radial
TurboMachines
(ANSYS)

ANNAPOLIS, MD
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Contents
List of Tables......................................................................................................................................................................... 6
List of Figures ....................................................................................................................................................................... 6

1 Introduction ................................................................................................................................ 11

2 Preliminary Concepts in Rotating Machinery ................................................................. 13

2.1 Vortex....................................................................................................................................................................... 13
2.2 Properties of Vortex Flow................................................................................................................................ 13
Vorticity ............................................................................................................................. 13
Vortex Types ...................................................................................................................... 14
2.2.2.1 A rigid-Body Vortex....................................................................................................... 14
2.2.2.2 Irrotational Vortex ........................................................................................................ 14
Vortex Geometry ............................................................................................................... 14
Pressure in Vortex ............................................................................................................. 15
2.3 Impeller ................................................................................................................................................................... 15
Types of Impeller ............................................................................................................... 16
Flow Characteristics for Impeller ....................................................................................... 16
Mixing Tanks ...................................................................................................................... 17
Axial Impellers ................................................................................................................... 18
Radial Impellers ................................................................................................................. 18
Power Number for Impeller............................................................................................... 18
2.4 Pumps ...................................................................................................................................................................... 18
Types of Pumps.................................................................................................................. 19
Axial-Flow Pumps vs. Centrifugal Pumps........................................................................... 20
2.5 Some Physics on Rotating Disks Flow ........................................................................................................ 20
Experimental Set-Up.......................................................................................................... 20
2.5.1.1 Recirculating Flow ........................................................................................................ 21
2.5.1.2 Instability Flow Patterns ............................................................................................... 21

3 Conservation of Angular Momentum ................................................................................. 24

3.1 Flow in Rotating Reference Frame .............................................................................................................. 24
Relative Velocity Formulation ........................................................................................... 25
Absolute Velocity Formulation .......................................................................................... 25
Early Formulation and Consideration ................................................................................ 25
3.2 Flows with Rotating Reference Frames ..................................................................................................... 26
Single Rotating Reference Frame (SRF) Modeling ............................................................. 26
Flow in Multiple Rotating Reference Frames (MRF) ......................................................... 27
3.2.2.1 Case Study – Mixing Tank ............................................................................................. 28
The MRF Interface Formulation......................................................................................... 28
3.2.3.1 Interface Treatment: Relative Velocity Formulation .................................................... 29
3.2.3.2 Interface Treatment: Absolute Velocity Formulation .................................................. 29
3.3 The Mixing Plane Model (MPM) .................................................................................................................... 29
Rotor and Stator Domains ................................................................................................. 30
The Mixing Plane Concept ................................................................................................. 30
Mixing Plane Algorithm ..................................................................................................... 31
3.3.3.1 Mass Conservation Across the Mixing Plane ................................................................ 31
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3.4 Sliding Mesh Modeling ...................................................................................................................................... 32

Sliding Mesh Theory .......................................................................................................... 32
The Sliding Mesh Technique .............................................................................................. 33
Sliding Mesh Concept ........................................................................................................ 34

4 Elements of Turbomachinery ............................................................................................... 35

4.1 Background............................................................................................................................................................ 35
4.2 Historical Perspectives ..................................................................................................................................... 36
4.3 Modern Turbomachinery as related to Gas Turbine Engine ............................................................. 36
4.4 Difference between Turbojet, Turbofan and Turboprop Engines in Aviation ........................... 37
Turbojet ............................................................................................................................. 38
Turbofan ............................................................................................................................ 38
Turboprop .......................................................................................................................... 39
How does it work? ............................................................................................................. 40
What is Thrust? .................................................................................................................. 41
4.5 Gas Turbine Performance ................................................................................................................................ 42
4.6 Gas Compressors ................................................................................................................................................. 43
Axial-flow compressors...................................................................................................... 43
Centrifugal Compressors ................................................................................................... 43
4.7 Nomenclature of Terms .................................................................................................................................... 44
4.8 Component of Gas Turbine Engine .............................................................................................................. 47
Inlet .................................................................................................................................... 47
Axial Compressor ............................................................................................................... 48
Diffuser .............................................................................................................................. 49
Nozzle ................................................................................................................................ 50
Combustor ......................................................................................................................... 50
Axial Gas Turbine ............................................................................................................... 51
4.9 Difference in Blading between Compressor and Turbine .................................................................. 52
4.10 Velocity Triangles in Turbomachines ......................................................................................................... 53
4.11 Energy Exchange with Moving Blades........................................................................................................ 54
Euler’s Equation for Turbomachinery ............................................................................... 54
4.12 Compressors and their Reaction to Intake Distortion ......................................................................... 56
4.13 Effects of Turbine Temperature.................................................................................................................... 57
4.14 Compressor and Turbine Characteristics ................................................................................................. 59
Stall ................................................................................................................................... 60
Compressor Surge.............................................................................................................. 60
Choked Flow ...................................................................................................................... 61

5 Primary Research in Turbomachinery.............................................................................. 62

5.1 Research Spectrum ............................................................................................................................................. 62
5.2 Application of CFD in Turbomachinery ..................................................................................................... 63
5.3 Quasi 3D Flow (Q3D) ......................................................................................................................................... 63
Stream Surface of Second Kind - Through Flow (S2) ......................................................... 64
Stream Surface of First Kind (Blade 2 Blade – S1) ............................................................. 65
Theory of Radial Equilibrium in Through Flow (Cr = 0) ...................................................... 66
5.4 Governing Equation of Rotating Frame of Reference .......................................................................... 67
5.5 Efficiency Effects in Turbomachinery......................................................................................................... 69
Isentropic Efficiency........................................................................................................... 69
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6 Complex Flow in Turbomachinery...................................................................................... 71

6.1 Key Features of Transonic Fan (Turbine) Field ..................................................................................... 71
6.2 Sources of Unsteadiness in Turbomachinery .......................................................................................... 72
6.3 Interaction of Potential Flows in Adjacent Blade Rows ...................................................................... 73
Interactions in Transonic Fan ............................................................................................ 74
6.4 Interaction between Wake Flow and Blade Rows ................................................................................. 75
6.5 Interaction between Secondary Flows and Blade Rows ..................................................................... 76
6.6 Wake-Boundary Layer Interaction .............................................................................................................. 77
6.7 Un-shrouded Tip Leakage Flow Interaction ............................................................................................ 78
6.8 Film Cooling Effects ............................................................................................................................................ 79
6.9 General Review on Secondary Flows .......................................................................................................... 79
Classical View ..................................................................................................................... 80
Modern View ..................................................................................................................... 80
Latest View ........................................................................................................................ 82
Comparing and Contrasting Secondry Flow in Turbine and Compressors ........................ 84
3D Separation .................................................................................................................... 85
6.10 Airfoil End-Wall Heat Transfer ...................................................................................................................... 87
Theoretical Development of End-Wall Flows .................................................................... 89
End-wall Heat Transfer ...................................................................................................... 90
End-wall Film-Cooling ........................................................................................................ 91
Leading Edge Modifications............................................................................................... 93
Blade Tip Heat Transfer ..................................................................................................... 94
Effects of Grid Refinement and Turbulence in 3D Flow Structure and End-wall Heat
Transfer in Transonic Turbine Blade Cascade ................................................................................... 95
6.10.6.1 Problem Definition ....................................................................................................... 96
6.10.6.2 Computational Aspects ................................................................................................ 96
6.10.6.3 Results and Discussion.................................................................................................. 98
6.10.6.4 End-Wall Heat Transfer Sensitivity w.r.t Grid and Turbulence Models........................ 98
6.10.6.5 Summary..................................................................................................................... 101
6.11 Discussion on Effects Swept and Dihedral Blades .............................................................................. 102
6.12 Blade Cooling ..................................................................................................................................................... 103
Blade Cooling Using Vanes in Blades ............................................................................... 104
6.12.1.1 VANE NASA C3X .......................................................................................................... 104
6.12.1.2 Showered Film Type Cooling ...................................................................................... 105
6.12.1.3 Complex Network of Vanes ........................................................................................ 105
Conjugate Heat Transfer.................................................................................................. 107
6.13 Case Study - Heat Transfer in Separated Flows on the P. S. of Turbine Blades ...................... 108
Literature Survey ............................................................................................................. 108
CFD Modeling .................................................................................................................. 109
Description of the Blade Computational Grids and Results for Attached Flow .............. 110
Separated Flow with Large Separation Bubble............................................................... 111
6.13.4.1 Inlet Flow Angle Effects .............................................................................................. 114
6.13.4.2 Reynolds Number Effect ............................................................................................. 115
Concluding Remarks ........................................................................................................ 117
6.14 General Perspectives on Turbulence Consideration ......................................................................... 118
Case Study - Turbulence Model Comparisons for a Low Pressure 1.5 Stage Test
Turbine 120
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7 Rotor-Stator Interaction Treatment (RST) ................................................................... 121

7.1 Physical Perspectives ..................................................................................................................................... 121
7.2 Multi-Passage vs. Multi-Stages ................................................................................................................... 122
7.3 Steady Treatment of Interface .................................................................................................................... 123
Mixing Plane .................................................................................................................... 123
Case Study - Modeling of Secondary Flows in Single Blade Rows using Mixing Plane
Approach......................................................................................................................................... 124
7.3.2.1 Statement and Background ........................................................................................ 124
7.3.2.2 Transonic Turbine Stage Meshing and Flow Details................................................... 125
Frozen Rotor .................................................................................................................... 126
7.4 Unsteady Treatment of Interface............................................................................................................... 127
Sliding Mesh (MRF) .......................................................................................................... 127
Non-Linear Harmonic Balanced Method (NLHB)............................................................. 129
Profile Transformation (Pitch Scaling) ............................................................................. 130
Time Transformation Method (TT) using Phase-Shifted Periodic Boundary Conditions 130
7.5 Revisiting Non-Linear Harmonic Balance (NLHB) Methodology ................................................. 132
Temporal and Spatial Periodicity Requirement............................................................... 133
Boundary Conditions ....................................................................................................... 133
Solution Method .............................................................................................................. 133
Fourier 'Shape Correction' for Single Passage Time-Marching Solution ......................... 135
Case Study 1 – 2D Compressor Stage .............................................................................. 136
Case Study 2 - 3D Flow in Turbine Cascade ..................................................................... 137

8 Radial Flow ............................................................................................................................... 139

8.1 Centrifugal Compressor................................................................................................................................. 139
Theory of operation ......................................................................................................... 139
Similarities to Axial Compressor ...................................................................................... 139
Components of a simple Centrifugal Compressor ........................................................... 140
8.1.3.1 Inlet ............................................................................................................................. 140
8.1.3.2 Centrifugal Impeller .................................................................................................... 140
8.1.3.3 Diffuser ....................................................................................................................... 141
8.1.3.4 Collector ..................................................................................................................... 141
Applications ..................................................................................................................... 142
8.1.4.1 In gas turbines and auxiliary power units................................................................... 142
8.1.4.2 Automotive engine and diesel engine turbochargers and superchargers ................. 142
8.1.4.3 Natural gas to move the gas from the production site to the consumer................... 142
8.1.4.4 Oil refineries, natural gas processing, petrochemical and chemical plants ............... 142
8.1.4.5 Air-conditioning and refrigeration and HVAC ............................................................ 142
8.1.4.6 In industry and manufacturing to supply compressed air.......................................... 143
8.1.4.7 In air separation plants to manufacture purified end product gases......................... 143
8.1.4.8 Oil field re-injection of high pressure natural gas to improve oil recovery ............... 143
8.2 Radial Turbine ................................................................................................................................................... 143
Advantages and challenges ............................................................................................. 144
Types of Radial Turbines .................................................................................................. 144
8.2.2.1 Cantilever Radial Turbine ........................................................................................... 144
8.2.2.2 90 Degree IFR Turbine ................................................................................................ 144
8.2.2.3 Outward-flow radial stages ........................................................................................ 145
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9 Best Practice Procedures for Turbomachinery ........................................................... 146

9.1 Quasi-3D (Q3D) or 3D Simulation ............................................................................................................. 146
2D Simulations ................................................................................................................. 146
Quasi-3D (Q3D) Simulation.............................................................................................. 146
Full 3D simulations .......................................................................................................... 146
9.2 Single vs Multi-Stage Analysis .................................................................................................................... 147
8.2.1 Single Stage ......................................................................................................... 147
Multi-Stage Analysis ........................................................................................................ 148
9.2.2.1 Steady Mixing-Plane simulations................................................................................ 148
9.2.2.2 Steady frozen rotor simulations ................................................................................. 148
9.2.2.3 Unsteady Sliding Mesh stator-rotor simulations........................................................ 148
9.2.2.4 Unsteady Harmonic Balance simulations ................................................................... 148
9.2.2.5 Hybrid steady-unsteady stator-rotor simulations ...................................................... 149
9.2.2.6 Other Advanced Multi-Stage Methods ...................................................................... 149
9.3 Inviscid or Viscid .............................................................................................................................................. 149
9.4 Transient or Steady-State ............................................................................................................................. 150
9.5 Meshing ................................................................................................................................................................ 152
Mesh Size Guidelines ....................................................................................................... 152
Case Study - Mesh Resolution Effect on 3D RANS Turbomachinery Flow Simulations ... 153
9.5.2.1 Formulation of Problems ............................................................................................ 154
9.5.2.2 Conclusions ................................................................................................................. 155
Boundary Mesh Resolution ............................................................................................. 155
Periodic Meshing ............................................................................................................. 155
9.6 Boundary Conditions ...................................................................................................................................... 156
9.7 Turbulence Modeling...................................................................................................................................... 158
9.8 Aero-Mechanics ................................................................................................................................................ 158
Nodal Diameter ............................................................................................................... 160
9.9 Near Wall Treatment ...................................................................................................................................... 160
9.10 Transition Prediction ..................................................................................................................................... 160
9.11 Numerical Consideration .............................................................................................................................. 161
9.12 Convergence Criteria ...................................................................................................................................... 161
9.13 Single or Double Precision ........................................................................................................................... 161
9.14 Heat Transfer Prediction .............................................................................................................................. 162
Keeping it Cool in Gas Turbine......................................................................................... 162
9.15 Literature Review and Parallel Processing Tools ............................................................................... 162
9.16 Concluding Remarks ....................................................................................................................................... 164

List of Tables
Table 3.1 Prescribed Boundary zone for Mixing Plane ..................................................................................... 31
Table 4.1 Glossary of Turbomachinery Terms ...................................................................................................... 44
Table 6.1 Parameters of the grids used .................................................................................................................... 97
Table 7.1 Rotor/Stator Interaction Schemes ...................................................................................................... 122

List of Figures
Figure 2.1 Vortex created by the passage of an aircraft wing, revealed by colored smoke ............... 13
Figure 2.2 A rigid-body vortex ..................................................................................................................................... 14
Figure 2.3 3D visualization of a vortex curves ...................................................................................................... 15
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Figure 2.4 A Plughole vortex ........................................................................................................................................ 15

Figure 2.5 Types of Impeller ......................................................................................................................................... 16
Figure 2.6 Flow direction of three different pumps/impellers. Image credit: Global spec ................. 17
Figure 2.7 A centrifugal pump uses an impeller with backward-swept arms ......................................... 17
Figure 2.8 Axial flow impeller (left) and radial flow impeller (right) ......................................................... 17
Figure 2.9 Centrifugal Pumps ....................................................................................................................................... 19
Figure 2.10 Sketch of the experimental set-up ..................................................................................................... 21
Figure 2.11 For s ≥ 0 co-rotation at different speed ........................................................................................... 22
Figure 2.12 For s < 0 counter-rotating at different speed ............................................................................... 23
Figure 3.1 Rotating Frame of Reference .................................................................................................................. 24
Figure 3.2 Single Blade Model with Rotationally Periodic Boundaries ...................................................... 27
Figure 3.3 Mixing Tank Geometry with one Rotating Impeller...................................................................... 27
Figure 3.4 Mixing Tank with two rotating impellers .......................................................................................... 28
Figure 3.5 Interface Treatment for the MRF Model ............................................................................................ 29
Figure 3.6 Mixing Plane Concepts as Applied to Axial Rotation .................................................................... 30
Figure 3.7 Mixing Plane Concepts Applied to Radial Rotation ....................................................................... 31
Figure 3.8 Illustration of Unsteady Interactions ................................................................................................... 32
Figure 3.9 Examples of Transient Interaction using Sliding Mesh ............................................................... 32
Figure 3.10 Initial position and some translation with Sliding Interface .................................................. 33
Figure 4.1 Classification of Turbomachines ........................................................................................................... 35
Figure 4.2 Component of Turbomachines and their Thermodynamic (Brayton cycle) properties . 37
Figure 4.3 Turbojet Engine............................................................................................................................................ 38
Figure 4.4 Turbofan Engine .......................................................................................................................................... 38
Figure 4.5 Turboprop Engine ....................................................................................................................................... 39
Figure 4.6 Turboshaft Engine ....................................................................................................................................... 39
Figure 4.7 Twin Pool Trubofan Jet Engine .............................................................................................................. 40
Figure 4.8 A 1D Control Volume around a propulsion system (Courtesy’s of NASA Glen Research
Center) ....................................................................................................................................................................................... 41
Figure 4.9 Gas Compressor Types .............................................................................................................................. 42
Figure 4.10 A single stage Centrifugal Compressor ............................................................................................ 43
Figure 4.11 Schematics of Axial Compressor......................................................................................................... 43
Figure 4.12 Blade Related Terminology .................................................................................................................. 47
Figure 4.13 Pressure and Velocity profile through a Multi-Stage Axial Compressor............................ 48
Figure 4.14 Compressor Flow Characteristics ...................................................................................................... 48
Figure 4.15 Combustor primary operating components .................................................................................. 51
Figure 4.16 Turbine Flow Characteristics............................................................................................................... 51
Figure 4.17 Schematics of axial flow Turbine........................................................................................................ 52
Figure 4.18 Examples of typical Blades for Compressor and Turbine ........................................................ 53
Figure 4.19 Velocity triangles for an Axial Compressor .................................................................................... 54
Figure 4.20 Velocity triangles in relation to incident angle ............................................................................. 55
Figure 4.21 Compressor operating map .................................................................................................................. 57
Figure 4.22 Sample engine Perssure, Velocity and Temperature variation ............................................. 58
Figure 4.23 Turbine Inlet Temperature27 ............................................................................................................... 59
Figure 4.24 Characteristics Graph of a Compressor ........................................................................................... 60
Figure 4.25 Classical Compressor surge cycles .................................................................................................... 60
Figure 4.26 Illustration of the propagation of a stall cell in the relative frame ....................................... 61
Figure 5.1 Impact of CFD on SNECMA fan performance, over a period of 30 years .............................. 62
Figure 5.2 Illustration of S1 and S2 surfaces ......................................................................................................... 64
Figure 5.3 Streamline Curvature Method................................................................................................................ 65
Figure 5.4 Radial Equilibrium ...................................................................................................................................... 67
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Figure 5.5 Coriolis and Centripetal forces created by the Rotating Frame of Reference .................... 68
Figure 5.6 Compression process ................................................................................................................................. 69
Figure 5.7 Expansion process ...................................................................................................................................... 69
Figure 6.1 Complex Flow phenomena compressors ........................................................................................... 71
Figure 6.2 Fan Tip section geometry......................................................................................................................... 72
Figure 6.3 Flow structures with 5 to 6 orders of magnitudes variations in length and time scales
....................................................................................................................................................................................................... 74
Figure 6.4 Shock Structure in Transonic Fan......................................................................................................... 75
Figure 6.5 Pressure Contour of Wake Flow ........................................................................................................... 76
Figure 6.6 Unsteady wakes convecting in blade passage ................................................................................. 76
Figure 6.7 Instantaneous absolute velocity contour pattern at nozzle exit .............................................. 77
Figure 6.8 Flow over an unshrouded tip gap ....................................................................................................... 78
Figure 6.9 Typical high-pressure turbine stage showing rim seal and wheel-space ............................ 79
Figure 6.10 Classical Secondary Flow Model ......................................................................................................... 81
Figure 6.11 Modern Secondary Flow Model .......................................................................................................... 82
Figure 6.12 Vortex pattern of Latest secondary flows ....................................................................................... 83
Figure 6.13 Turbine Secondary Flow Model (Takeishi et al.) ........................................................................ 84
Figure 6.14 Illustration of formation of hub corner stall together with..................................................... 86
Figure 6.15 Illustration of the near wall flows as taken through oil and dye surface flow
visualization (reproduced with permission of the publisher from ASME) .................................................. 87
Figure 6.16 Classic Secondary flow pattern for a turbine airfoil passage (L. S. Langston)................. 87
Figure 6.17 (Top)-Measurements of the horseshoe vortex just .................................................................... 88
Figure 6.18 Illustration of different vortical .......................................................................................................... 89
Figure 6.19 Contours of non-dimensional heat transfer coefficients (reproduced with ASME)...... 90
Figure 6.20 Measured adiabatic wall temperatures for coolant exiting a combustor/vane leakage
slot (reproduced with permission from ASME)........................................................................................................ 91
Figure 6.21 Contours of adiabatic effectiveness for two film-cooling hole patterns (left and center)
with a mid-passage gutter for the cooling hole pattern in the center (right) (reproduced with
permission from the publisher of ASME) .................................................................................................................... 93
Figure 6.22 fillet and bulb designs as shown by (Becz et al.)........................................................................... 94
Figure 6.23 CFD prediction of streamlines across a ........................................................................................... 95
Figure 6.24 Blade passage and slice of the computational domain .............................................................. 96
Figure 6.25 Computed mid-span Mach number distribution ......................................................................... 98
Figure 6.26 End-wall Stanton number (103) distributions computed with grid B in comparison
with the measurement data: (1) k-ω turbulence model, (2) M-SST, (3) v2-f, (4) Experiment .......... 99
Figure 6.27 Effect of grid refinement on the end-wall Stanton number (x103) prediction with the
M-SST turbulence model: (1) grid С, (2) grid D, (3) grid E, (4) experiment. ............................................. 100
Figure 6.28 End-wall streak line visualization................................................................................................... 101
Figure 6.29 Geometry of Swept and Dihedral Blades ..................................................................................... 102
Figure 6.30 Experimental Pressure iso-surfaces ; Left - without sweep ;Right - with forward
sweep. Courtesy of RÁBAI and VAD [93] .................................................................................................................. 103
Figure 6.31 The schematic of a modern gas turbine blade with common cooling techniques
(Courtesy of Je-Chin Han) ................................................................................................................................................ 103
Figure 6.32 Vane section with ten cooling channels and Temperature distribution computed ... 104
Figure 6.33 Surface temperature distribution on the suction side (left) and the pressure side
(right) of the vane............................................................................................................................................................... 105
Figure 6.34 Flow Streamlines Colored Cooling Air Temperature into Passages ................................. 106
Figure 6.35 Profile view of showerhead film cooled vane ............................................................................ 106
Figure 6.36 CAD model of simulated blade (left) and its internal passages (right) ........................... 107
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Figure 6.37 T106-300 Cascade geometry and aerodynamic design conditions (Courtesy of De La
Calzada et al.) ....................................................................................................................................................................... 110
Figure 6.38 2-D hybrid mesh around the T106 blade .................................................................................... 111
Figure 6.39 Blade profile vs. pressure coefficient (Courtesy of De La Calzada et al.) ........................ 111
Figure 6.40 Flow field at the front and middle parts of the separation bubble (Courtesy of De La
Calzada et al.) ....................................................................................................................................................................... 112
Figure 6.41 Heat Transfer Coefficient for different negative incidences (Courtesy of Calzada et al.)
.................................................................................................................................................................................................... 114
Figure 6.42 Stanton number for different negative incidences (Courtesy of De La Calzada et al.)
.................................................................................................................................................................................................... 115
Figure 6.43 Stanton Number Vs. Reynolds Numbers (Courtesy of De La Calzada et al.) ................. 116
Figure 6.44 Heat Transfer Coefficient Vs. Reynolds Number (Courtesy of Calzada et al.) .............. 116
Figure 6.45 Pressure Ratio by Normalized Mass Flow (Courtesy of Simoes) ....................................... 118
Figure 7.1 Schematics of 3D concept at IGV/Rotor/Stator interface........................................................ 121
Figure 7.2 Interface between Rotor/Stator ......................................................................................................... 122
Figure 7.3 Difference between Passage and Stages ......................................................................................... 122
Figure 7.4 Axial Rotor/Stator Interaction (Schematics Illustrating the Mixing Plane concepts) . 123
Figure 7.5 Block Computational domain for a Rotor with guiding vanes ............................................... 123
Figure 7.6 A compressor Pressure Distribution on a surface using a Mixing Plane ........................... 124
Figure 7.7 Mesh for Transonic Turbine Stage - Upper Image Depicted the Mesh at the Hub Surface
while the Lower Image Represented Mesh used for the Blade Span ............................................................ 125
Figure 7.8 Results of the Velocity Contours for a Radial Section at Stator Mid Span using the
Mixing Plane Approach .................................................................................................................................................... 126
Figure 7.9 Total Pressure Calculated by the Frozen Rotor ........................................................................... 127
Figure 7.10 Half stencil and full stencil reconstruction with: A) Intersection, B) Halo-cell............ 128
Figure 7.11 Relative velocities obtained using HB techniques ................................................................... 129
Figure 7.12 Phase shifted Periodic Boundary .................................................................................................... 130
Figure 7.13 Phase Shifted Periodic Boundary Conditions............................................................................. 131
Figure 7.14 Stagnation Pressure Contours under inlet distortion for NASA Rotor 67 ..................... 136
Figure 7.15 Computational mesh for HB and TRS methods ........................................................................ 136
Figure 7.16 Instantaneous pressure distribution within the compressor stage using (NLHB) .... 137
Figure 7.17 Instantaneous predictions of turbulent viscosity at mid-span turbine for the TRS... 137
Figure 7.18 Instantaneous predictions of turbulent viscosity at mid-span turbine for the HB .... 138
Figure 7.19 velocity profile on interface line between two rows............................................................... 138
Figure 8.1 Centrifugal impeller with a highly polished surface likely to improve performance .. 139
Figure 8.2 Cut-Away View of a Turbocharger showing the Centrifugal Compressor ........................ 140
Figure 8.3 Jet engine cutaway showing the centrifugal compressor and other parts. ...................... 141
Figure 8.4 Ninety degree inward-flow radial turbine stage ......................................................................... 143
Figure 8.5 Outward Flow Radial Turbine ............................................................................................................. 144
Figure 9.1 Different Flow (2D, Q3D, and full 3D) .............................................................................................. 147
Figure 9.2 Full Blade Simulation using Harmonic Balanced Method (Courtesy of CD-adapco) .... 149
Figure 9.3 Transient Blade Row extensions enable efficient multi-stage CFD simulation (Courtesy
of ANSYS.com) ..................................................................................................................................................................... 151
Figure 9.4 Typical meshing of a Turbomachinery stage ................................................................................ 152
Figure 9.5 Multi-block grid for the space shuttle main engine fuel Turbine ......................................... 153
Figure 9.6 Pressure contour plot, 2nd order spatial discretization scheme.......................................... 157
Figure 9.7 Analysis provided vibration required for flutter analysis ....................................................... 159
Figure 9.8 Examples of Nodal Diameter ............................................................................................................... 160