Wind Turbine Aerodynamics and Vorticity-Based Methods: Fundamentals and Recent Applications (Research Topics in Wind Energy Book 7)

The book introduces the fundamentals of fluid-mechanics, momentum theories, vortex theories and vortex methods necessary for the study of rotors aerodynamics and wind-turbines aerodynamics in particular. Rotor theories are presented in a great level of details at the beginning of the book. These theories include: the blade element theory, the Kutta-Joukowski theory, the momentum theory and the blade element momentum method. A part of the book is dedicated to the description and implementation of vortex methods. The remaining of the book focuses on the study of wind turbine aerodynamics using vortex-theory analyses or vortex-methods. Examples of vortex-theory applications are: optimal rotor design, tip-loss corrections, yaw-models and dynamic inflow models. Historical derivations and recent extensions of the models are presented. The cylindrical vortex model is another example of a simple analytical vortex model presented in this book. This model leads to the development of different BEM models and it is also used to provide the analytical velocity field upstream of a turbine or a wind farm under aligned or yawed conditions. Different applications of numerical vortex methods are presented. Numerical methods are used for instance to investigate the influence of a wind turbine on the incoming turbulence. Sheared inflows and aero-elastic simulations are investigated using vortex methods for the first time. Many analytical flows are derived in details: vortex rings, vortex cylinders, Hill's vortex, vortex blobs etc. They are used throughout the book to devise simple rotor models or to validate the implementation of numerical methods. Several Matlab programs are provided to ease some of the most complex implementations. Front Matter....Pages i-xxxi Introduction....Pages 1-7 Front Matter....Pages 9-9 Theoretical Foundations for Flows Involving Vorticity....Pages 11-82 Lifting Bodies and Circulation....Pages 83-110 Front Matter....Pages 111-111 Rotor and Wind Turbine Formalism....Pages 113-119 Vortex Systems and Models of a Rotor - Bound, Root and Wake Vorticity....Pages 121-133 Considerations and Challenges Specific to Rotor Aerodynamics....Pages 135-141 Blade Element Theory (BET)....Pages 143-149 Kutta–Joukowski (KJ) Theorem Applied to a Rotor....Pages 151-156 Momentum Theory....Pages 157-180 The Blade Element Momentum (BEM) Method....Pages 181-211 Front Matter....Pages 213-213 Far-Wake Analyses and the Rigid Helical Wake....Pages 215-222 Betz Theory of Optimal Circulation....Pages 223-225 Tip-Losses with Focus on Prandlt’s Tip Loss Factor....Pages 227-245 Goldstein’s Optimal Circulation....Pages 247-253 Wake Expansion Models....Pages 255-258 Relation Between Far-Wake and Near-Wake Parameters....Pages 259-262 Front Matter....Pages 263-263 Cylindrical Vortex Model of a Rotor of Finite or Infinite Tip-Speed Ratios....Pages 265-272 Cylindrical Model of a Rotor with Varying Circulation - Effect of Wake Rotation....Pages 273-282 An Improved BEM Algorithm Accounting for Wake Rotation Effects....Pages 283-291 Helical Model for Tip-Losses: Development of a Novel Tip-Loss Factor and Analysis of the Effect of Wake Expansion....Pages 293-297 Front Matter....Pages 263-263 Yaw-Modelling Using a Skewed Vortex Cylinder....Pages 299-306 Simple Implementation of a New Yaw-Model....Pages 307-313 Advanced Implementation of the New Yaw-Model....Pages 315-320 Velocity Field Upstream of Aligned and Yawed Rotors: Wind Turbine and Wind Farm Induction Zone....Pages 321-332 Analytical Model of a Wind Turbine in Sheared Inflow....Pages 333-337 Model of a Wind Turbine with Unsteady Circulation or Unsteady Inflow....Pages 339-344 Front Matter....Pages 345-345 Examples of Applications of Vortex Methods to Wind Energy....Pages 347-353 Representation of a (Turbulent) Velocity Field Using Vortex Particles....Pages 355-360 Effect of a Wind Turbine on the Turbulent Inflow....Pages 361-369 Aeroelastic Simulation of a Wind Turbine Under Turbulent and Sheared Conditions....Pages 371-378 Front Matter....Pages 379-379 Elementary Three-Dimensional Flows....Pages 381-392 Elementary Two-Dimensional Potential Flows....Pages 393-400 Flows with a Spread Distribution of Vorticity....Pages 401-406 Spherical Geometry Models: Flow About a Sphere and Hill’s Vortex....Pages 407-417 Vortex and Source Rings....Pages 419-428 Flow Induced by a Right Vortex Cylinder....Pages 429-453 Flow Induced by a Vortex Disk....Pages 455-460 Flow Induced by a Skewed Vortex Cylinder....Pages 461-471 Flow Induced by Helical Vortex Filaments....Pages 473-479 Front Matter....Pages 481-481 A Brief Introduction to Vortex Methods....Pages 483-492 Front Matter....Pages 481-481 The Different Aspects of Vortex Methods....Pages 493-543 Particularities of Vortex Particle Methods....Pages 545-551 Numerical Implementation of Vortex Methods....Pages 553-573 OmniVor: An Example of Vortex Code Implementation....Pages 575-586 Vortex Code Validation and Illustration....Pages 587-593 Back Matter....Pages 595-632