The first rotor performance predictions were published by Joukowsky exactly 100 years ago. Although a century of research has expanded the knowledge of rotor aerodynamics enormously, and modern computer power and measurement techniques now enable detailed analyses that were previously out of reach, the concepts proposed by Froude, Betz, Joukowsky and Glauert for modelling a rotor in performance calculations are still in use today, albeit with modifications and expansions. This book is the result of the author's curiosity as to whether a return to these models with a combination of mathematics, dedicated computations and wind tunnel experiments could yield more physical insight and answer some of the old questions still waiting to be resolved. Although most of the work included here has been published previously, the book connects the various topics, linking them in a coherent storyline. “The Fluid Dynamic Basis for Actuator Disc and Rotor Theories” was first published in 2018. This Revised Second Edition (2022) will be of interest to those working in all branches of rotor aerodynamics – wind turbines, propellers, ship screws and helicopter rotors. It has been written for proficient students and researchers, and reading it will demand a good knowledge of inviscid (fluid) mechanics. Jens Nørkær Sørensen, DTU, Technical University of Denmark: “(…) a great piece of work, which in a consistent way highlights many of the items that the author has worked on through the years. All in all, an impressive contribution to the classical work on propellers/wind turbines.” Peter Schaffarczyk, Kiel University of Applied Sciences, Germany: “(…) a really impressive piece of work!” Carlos Simão Ferreira, Technical University Delft: “This is a timely book for a new generation of rotor aerodynamicists from wind turbines to drones and personal air-vehicles. In a time where fast numerical solutions for aerodynamic design are increasingly available, a clear theoretical and fundamental formulation of the rotor-wake problem will help professionals to evaluate the validity of their design problem. ‘The Fluid Dynamic Basis for Actuator Disc and Rotor Theories’ is a pleasure to read, while the structure, text and figures are just as elegant as the theory presented.” The cover shows ‘The Red Mill’, by Piet Mondriaan, 1911, collection Gemeentemuseum Den Haag. Cover image: © 2022 Mondrian/Holtzman Trust.
Author(s): Gijs van Kuik
Edition: 2
Publisher: IOS Press
Year: 2022
Language: English
Pages: 161
City: Amsterdam
Title Page
Preface
Reading guide
Acknowledgement
Nomenclature
More than a century of rotor research
Introduction
History of the actuator disc momentum theory
The British School
The German and Russian School
The contribution of Joukowsky and Betz to the vortex theory of propellers
The Betz-Joukowsky limit for wind turbines
From actuator disc to rotor aerodynamics
Why this book?
Force fields in fluid dynamics
Introduction
The equation of motion and the coordinate systems
Equivalence of the kinematic and dynamic methods
Conservative and non-conservative force fields
Force fields and energy
Work done by force fields
Choice of reference system
Work done by non-conservative force fields
Pressure as a conservative force in momentum balances
Pressure interpreted as potential energy
Definition of (non-)conservative forces as used in this book
Evaluation
Force fields and vorticity
Introduction
The role of Helmholtz's conservation laws
Generation of actuator disc vorticity
Convection of actuator disc vorticity
Convection of rotor vorticity
Evaluation
The disc as representation of a rotor
Introduction
Loads and power of a Joukowsky disc and rotor
The actuator disc equation
The rotor blade
Power and thrust coefficients for Joukowsky discs / rotors
The transition from a B-bladed rotor to the Joukowsky disc
Comparison of the flow fields of a disc and rotor
Evaluation
Analysis of Froude's actuator disc flows
Introduction
One-dimensional momentum theory
The momentum balance
Momentum theory without conservative forces
Momentum theory including conservative forces, applied to a stream annulus
Numerical assessment of Froude's actuator disc performance
The model and accuracy of computation
Comparison of calculated performance with momentum theory results
Comparison with experimental results
Flow details
Flow and pressure patterns
Properties of the wake boundary
Pressure and velocity at the disc
Pressure at the axis
Evaluation
Analysis of Joukowsky's actuator disc flows
Introduction
Two-dimensional momentum theory
The equations for a Joukowsky disc
The disc load
The far wake outside the vortex core
The vortex core
The momentum, mass and energy balance
Limit values of the Joukowsky momentum theory
Results for , 0.
Propeller discs with a wake of constant radius or with wake expansion
The static disc or disc in hover
The maximum efficiency of a wind turbine disc
The efficiency of propeller discs
Numerical assessment of flow details
The numerical model
Comparison of wind turbine and propeller discs at =1
Comparison of a wind turbine and propeller disc with similar wake expansion
The role of swirl and conservative pressure distributions
Comparison of the Joukowsky and Betz-Goldstein solutions
Evaluation
The velocity distribution at the disc
Introduction
The absolute velocity
Wind turbine flows
Propeller flows
Explanation of the (non-)uniformity of vs
The axial velocity
Momentum balance per annulus
An engineering model for the axial velocity at a high wind turbine disc
The radial velocity
Evaluation
Special topics: cons. loads at a thick disc & blade tip
Introduction
The generation of a Rankine vortex
Wu's actuator disc equation
The force field required to generate a Rankine vortex
Interpretation of the radial component of the load
Numerical assessment of the impact of the radial load
The rotor blade
Inboard motion of a tip vortex of a wind turbine blade
Side step: conservative, spanwise load on an elliptic wing
Conservative and non-conservative blade loads
Experimental and numerical results for a model wind turbine rotor
Determination of the conservative tip load
The tip vortex trajectory
The role of conservative forces
Evaluation
From disc theory to BEM models: the tip correction
Introduction
Development of the tip correction
In BEM methods
In actuator disc, actuator line and lifting line methods
The distribution of the axial velocity
The radial distribution
The azimuthal distribution: averaged or at blade position
The azimuthal distribution: decambering of aerofoils
The radial distribution of blade
The aspect ratio as a measure for tip effects
Conservative tip load and the tip vortex trajectory
Evaluation
Epilogue
Vector expressions in cylindrical coordinates
Balance of angular momentum
The blade load expressed as pressure distribution
The potential flow model
Components of the model
Convergence scheme
Verification, sensitivity and accuracy
Bibliography
Index
