An Algorithm for the Aerodynamic Analysis of Rotating Blades Using a Weak Viscous-Inviscid ...

213 Pages·2013·8.56 MB·English

An Algorithm for the Aerodynamic Analysis of Rotating
Blades Using a Weak Viscous-Inviscid Interaction Method
by
Mengu Umut Tinis
A thesis submitted to the Faculty of Graduate and Postdoctoral
Affairs in partial fulfillment of the requirements for the degree of
Master of Applied Science
in
Aerospace Engineering
Carleton University
Ottawa, Ontario
©2013
Mengu Umut Tinis
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Abstract
An algorithm based on a weak viscous-inviscid interaction method is developed
for the aerodynamic analysis of rotating blades under steady and incompressible flow
conditions for configurations where the aerodynamics of each blade can be treated in
isolation. A weak viscous-inviscid interaction method for calculating the aerodynamics of
airfoil geometries, which is based on a two-dimensional source-vortex panel method and
the momentum-integral method, is updated using state-of-the-art models and correlations
to predict specific flow phenomena such as transitioning flow and separated flow. The
blade-element-momentum theory with Prandtl root- and tip-loss corrections is used to
calculate the three-dimensional aerodynamics of rotating blades, using the two-
dimensional aerodynamic predictions of the viscous-inviscid interaction method and
empirical stall delay models. The algorithm is shown to provide predictions that are
sufficiently accurate for blade design optimization under unstalled operating conditions.
The accuracy of the algorithm is limited to about 3° ~ 5° angle of attack beyond stall.
Acknowledgements
First and foremost, I would like to thank my thesis supervisors, Drs. Metin I.
Yaras, Fred F. Afagh, and Robert G. Langlois for providing me with this wonderful
opportunity to work in my area of interest and on a project which offers unlimited
learning opportunities. I thank Dr. Yaras for his constant guidance, motivation, and
advice, which have been invaluable throughout this study. The many hours of discussion
we had are greatly appreciated. 1 would like to thank Drs. Afagh and Langlois for staying
on board and supporting this study until completion even after the focus of the study
shifted away from their primary area of interest. 1 would also like to acknowledge all my
colleagues and friends in Dr. Yaras’ research group for their support and feedback during
my studies, and particularly Joshua Brinkerhoff for his instrumental suggestions to help
me bring this manuscript to completion.
My greatest thanks go to my father, Rait Tinis, my mother, Fusun Tinis, and my
better half, Esra Merdimeydan. Without their love, support, and encouragement, this
accomplishment would not have been possible.
Table of Contents
Abstract.............................................................................................................................ii
Acknowledgements..........................................................................................................iii
Table of Contents.............................................................................................................iv
List of Tables....................................................................................................................x
List of Figures..................................................................................................................xi
Nomenclature..................................................................................................................xv
Chapter 1: Introduction...................................................................................................1
1.1 Motivation.............................................................................................................1
1.2 Objectives..............................................................................................................2
1.3 Approach...............................................................................................................3
Chapter 2: Background Information on Rotating Blade Aerodynamics....................4
2.1 Aerodynamic Working Principle of Wind Turbine and Propeller Blades.............4
2.2 Methods for Calculating Turbomachinery Performance.......................................6
2.2.1 Momentum (Actuator Disc) Theory................................................................7
2.2.2 Blade-Element Theory (BET)........................................................................12
2.2.3 Blade-Element-Momentum Theory (BEMT)................................................15
2.3 Governing Equations of Fluid Dynamics.............................................................18
2.4 Inviscid Flow........................................................................................................19
2.4.1 Euler Equations..............................................................................................19
2.4.2 Potential Flow Equations...............................................................................20
2.4.3 Potential-Flow-Singularity Methods.............................................................21
2.5 Viscous Flow.......................................................................................................22
2.5.1 Boundary-Layer Equations............................................................................22
2.5.2 The Momentum-Integral Relation.................................................................26
2.5.2.1 Laminar Closure Method......................................................................28
2.5.2.2 Turbulent Closure Method....................................................................29
Chapter 3: Literature Review............................................................................................32
3.1 Analysis Methods for Turbomachinery Performance and Aerodynamics..........32
3.1.1 Momentum (Actuator Disc) Theory..............................................................32
3.1.2 Blade-Element Theory (BET)........................................................................33
3.1.3 Blade-Element-Momentum Theory (BEMT)................................................34
3.1.4 Navier-Stokes Equation Solutions.................................................................36
3.1.5 Viscous-inviscid Interaction (VII)................................................................38
3.2 Inviscid Flow Analysis Methods........................................................................45
3.2.1 Thin Airfoil Theory (TAT)............................................................................46
3.2.2 Lifting-Line Blade Model..............................................................................47
3.2.3 Surface Singularity (Panel) Methods............................................................49
3.2.3.1 3D Panel Methods................................................................................52
3.2.3.2 2D Panel Methods................................................................................54
3.3 Viscous Flow Analysis Methods........................................................................54
3.3.1 Similarity Solutions for the Boundary-Layer Equations................................55
3.3.2 Alternative Analysis Methods for Boundary Layers......................................57
3.3.2.1 Integral Methods..................................................................................58
3.3.3 Flow Transition.............................................................................................60
3.3.3.1 Modes of Flow Transition....................................................................60
v
3.3.3.2 Factors Influencing Flow Transition....................................................62
3.3.3.3 Transition Models................................................................................63
3.3.4 Flow Separation............................................................................................66
3.4 Additional Aerodynamic Effects for Consideration..........................................68
3.4.1 Lift-Induced Velocity....................................................................................68
3.4.2 Lift Loss at the Blade Root and Tip..............................................................68
3.4.3 Unsteady Aerodynamic Effects......................................................................69
3.4.3.1 Corrigan-Schillings Stall Delay Model................................................71
3.4.3.2 “Centrifugal Pumping” Model of Lindenburg........................... 73
3.4.4 Rotor Wake Effects.......................................................................................74
3.4.5 Wind Shear.....................................................................................................76
3.4.6 Streamwise Surface Curvature.......................................................................78
Chapter 4: Algorithm for the Aerodynamic Analysis of Rotating Blades..................80
4.1 Introduction........................................................................................................80
4.2 A Weak Viscous-inviscid Interaction Method for Steady, 2D,I ncompressible
Flow around an Airfoil.................................................................................................80
4.2.1 Inviscid Flow Analysis Using a 2D Source-Vortex Panel Method................81
4.2.1.1 Discretization for the 2D Panel Method...............................................81
4.2.1.2 Boundary Conditions............................................................................83
4.2.1.3 System of Equations.............................................................................87
4.2.1.4 Inviscid Flow Velocity and Pressure Coefficient Distribution..............89
4.2.1.5 Sizing of Airfoil Surface Panels............................................................90
4.2.2 Viscous Flow Analysis Using the Momentum-Integral Relation..................92
4.2.2.1 The Momentum-Integral Relation.......................................................92
4.2.2.2 Solution Grid for the Viscous Flow Analysis......................................94
4.2.2.3 Laminar Momentum-Integral Calculation...........................................95
4.2.2.4 Turbulent Momentum-Integral Calculation.........................................97
4.2.2.5 Transition Model...............................................................................100
4.2.2.6 Calculation of the Boundary-Layer Parameters.................................105
4.2.2.6.1 Calculation of the Boundary-Layer Parameters in an Attached-
Flow Transition Region...............................................................................105
4.2.2.6.2 Calculation of the Boundary-Layer Parameters in a Separated-Flow
Transition Region.........................................................................................107
4.2.2.7 Treatment of Flow Separation................................................... 109
4.2.3 Calculation of the 2D Aerodynamic Coefficients..................................................113
4.2.4 Interfacing of the Viscous and Inviscid Flow Solutions...............................116
4.3 Calculation of the 3D Aerodynamics of Rotating Blades.................................119
4.3.1 Application of the Blade-Element-Momentum Theory for the 3D
Aerodynamic Analysis of Wind Turbine Blades...................................................120
4.3.1.1 Calculation of Induced Velocity for Wind Turbine Blades................121
4.3.1.2 Calculation of the Effective Angle of Attack.....................................123
4.3.2 Application of the Blade-Element-Momentum Theory for the 3D
Aerodynamic Analysis of Propeller Blades...........................................................124
4.3.2.1 Calculation of the Induced Velocity in Propeller Blades....................124
4.3.2.2 Calculation of the Effective Angle of Attack.....................................127
4.3.3 Stall Delay Corrections................................................................................128
4.4 Calculation of Rotor Performance....................................................................129
Chapter 5: Verification and Validation..........................................................................131
5.1 Inviscid Flow Analysis Algorithm....................................................................131
5.2 Viscous flow Analysis Algorithm.....................................................................132
5.2.1 Laminar Momentum-Integral Predictions....................................................132
5.2.2 Turbulent Momentum-Integral Predictions.................................................133
5.2.3 Boundary Layers with Attached-Flow Transition........................................136
5.3 Weak Viscous-inviscid Interaction Algorithm for Predicting 2D Airfoil
Performance...............................................................................................................139
5.3.1 S809 Airfoil.................................................................................................140
5.3.1.1 Airfoil Surface Pressure Distributions...............................................140
5.3.1.2 Lift Coefficient...................................................................................144
5.3.1.3 Drag Coefficient.................................................................................146
5.3.1.4 Pitching-Moment Coefficient.............................................................147
5.3.2 NACA 0012 Airfoil.....................................................................................148
5.3.2.1 Airfoil Surface Pressure Distributions................................................148
5.3.2.2 Lift Coefficient...................................................................................150
5.3.2.3 Drag Coefficient.................................................................................150
5.3.2.4 Pitching-Moment Coefficient.............................................................151
5.4 Aerodynamic Loads and Performance of a Rotating Wind Turbine Blade 152
5.4.1 Normal and Tangential Forces.....................................................................154
5.4.2 Pitching Moment.........................................................................................158
5.5 Computation Time............................................................................................159
Chapter 6: Conclusions and Future Work....................................................................161
6.1 Conclusions......................................................................................................161
6.2 Future Work......................................................................................................162
Appendices...........................................................................................................................163
Appendix A: Flowchart of the Present Aerodynamic Analysis Algorithm..............163
Appendix B: Coordinates for the S809 and NACA 0012 Airfoils.........................167
B.l S809 Airfoil.................................................................................................167
B.2 NACA 0012 Airfoil.....................................................................................170
References............................................................................................................................175
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