Preface Acknowledgements Introduction: Modern wind energy and its origins Modern wind turbines History of wind energy Wind characteristics and resources Introduction General characteristics of the wind resource Characteristics of the atmospheric boundary layer Wind data analysis and resource estimation Wind turbine energy production estimates using statistical techniques Overview of available resource assessment data Wind measurements and instrumentation Advanced topics Aerodynamics of wind turbines General overview One-dimensional momentum theory and the Betz limit Ideal horizontal axis wind turbing with wake rotation' Airfoils and general concepts of aerodynamics Momentum theory and blade element theory Blade shape for ideal rotor without wake rotation General rotor blade shape performance prediction Blade shape for optimum rotor with wake rotation Generalized rotor design procedure Simplified HAWT rotor performance calculation procedure Effect of drag and blade number on optimum performance Advanced aerodynamic topics Mechanics and dynamics Wind turbine rotor dynamics Detailed and specialized dynamic models Electrical aspects of wind turbines Basic concepts of electric power Power transformers Electrical machines Power converters Ancillary electrical equipment Wind turbine design Design procedure Wind turbine topologies Materials Machine elements Wind turbine loads Wind turbine subsystems and components Design evaluation Power curve prediction Wind turbine loads Wind turbine subsystems and components Design evaluation Power curve prediction Wind turbine control Overview of wind turbine control systems Typical grid-connected turbine operation Supervisory control overview and implementation Dynamic control theory and implementation Wind turbine siting, system design and integration Wind turbine siting Installation and operation issues Wind farms Wind turbines and wind farms in electric grids Offshore wind farms Operation in severe climates Hybrid electrical systems Wind energy system economics Overview of economic assessment of wind energy systems Capital costs of wind energy systems Operation and maintenance costs Value of wind energy Economic analysis methods Wind energy market considerations Wind energy systems: environmental aspects and impacts Avian interaction with wind trubines Visual impact of wind turbines Wind turbine noise Electromagnetic interference effects Land-use environmental impacts Other environmental considerations Nomenclature Problems Index

Wind energy explained : theory, design, and application

A review of conduction phenomena in Li-ion batteries

A critical review of the intrinsic nature of vortex-induced vibrations

In this paper a lattice Boltzmann (LB) model to simulate incompressible flow is developed. The main idea is to explicitly eliminate the terms of o(M
2), where M is the Mach number, due to the density fluctuation in the existing LB models. In the proposed incompressible LB model, the pressure p instead of the mass density ρ is the independent dynamic variable. The incompressible Navier–Stokes equations are derived from the incompressible LB model via Chapman–Enskog procedure. Numerical results of simulations of the plane Poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2D Womersley flow are presented. The numerical results are found to be in excellent agreement with theory.

Lattice boltzmann model for the incompressible navier-stokes equation

In this paper, we study the transverse vortex-induced vibrations of an elastically mounted rigid cylinder in a fluid flow. We use simultaneous force, displacement and vorticity measurements (using DPIV) for the first time in free vibrations. There exist two distinct types of response in such systems, depending on whether one has a high or low combined mass–damping parameter (m*ζ). In the classical high-(m*ζ) case, an ‘initial’ and ‘lower’ amplitude branch are separated by a discontinuous mode transition, whereas in the case of low (m*ζ), a further higher-amplitude ‘upper’ branch of response appears, and there exist two mode transitions.To understand the existence of more than one mode transition for low (m*ζ), we employ two distinct formulations of the equation of motion, one of which uses the ‘total force’, while the other uses the ‘vortex force’, which is related only to the dynamics of vorticity. The first mode transition involves a jump in ‘vortex phase’ (between vortex force and displacement), ϕvortex, at which point the frequency of oscillation (f) passes through the natural frequency of the system in the fluid, f ∼ fNwater. This transition is associated with a jump between 2S [harr ] 2P vortex wake modes, and a corresponding switch in vortex shedding timing. Across the second mode transition, there is a jump in ‘total phase’, phis;total , at which point f ∼ fNvacuum. In this case, there is no jump in ϕvortex, since both branches are associated with the 2P mode, and there is therefore no switch in timing of shedding, contrary to previous assumptions. Interestingly, for the high-(m*ζ) case, the vibration frequency jumps across both fNwater and fNvacuum, corresponding to the simultaneous jumps in ϕvortex and ϕtotal. This causes a switch in the timing of shedding, coincident with the ‘total phase’ jump, in agreement with previous assumptions.For large mass ratios, m* = O(100), the vibration frequency for synchronization lies close to the natural frequency (f* = f/fN ≈ 1.0), but as mass is reduced to m* = O(1), f* can reach remarkably large values. We deduce an expression for the frequency of the lower-branch vibration, as follows:formula herewhich agrees very well with a wide set of experimental data. This frequency equation uncovers the existence of a critical mass ratio, where the frequency f* becomes large: m*crit = 0.54. When m* < m*crit, the lower branch can never be reached and it ceases to exist. The upper-branch large-amplitude vibrations persist for all velocities, no matter how high, and the frequency increases indefinitely with flow velocity. Experiments at m* < m*crit show that the upper-branch vibrations continue to the limits (in flow speed) of our facility.

Modes of vortex formation and frequency response of a freely vibrating cylinder

GOVERNING EQUATIONS Basic Conservation Laws . Statistical and Continuum Methods . Eulerian and Lagrangian Coordinates . Material Derivative . Control Volumes . Reynolds' Transport Theorem . Conservation of Mass . Conservation of Momentum . Conservation of Energy . Discussion of Conservation Equations . Rotation and Rate of Shear . Constitutive Equations . Viscosity Coefficients . Navier-Stokes Equations . Energy Equation . Governing Equations for Newtonian Fluids . Boundary Conditions Flow Kinematics . Flow Lines . Circulation and Vorticity . Stream Tubes and Vortex Tubes . Kinematics of Vortex Lines Special Forms of the Governing Equations . Kelvin's Theorem . Bernoulli Equation . Crocco's Equation . Vorticity Equation IDEAL-FLUID FLOW Two-Dimensional Potential Flows . Stream Function . Complex Potential and Complex Velocity . Uniform Flows . Source, Sink, and Vortex Flows . Flow in a Sector . Flow Around a Sharp Edge . Flow Due to a Doublet . Circular Cylinder Without Circulation . Circular Cylinder With Circulation . Blasius' Integral Law . Force and Moment on a Circular Cylinder . Conformal Transformations . Joukowski Transformation . Flow Around Ellipses . Kutta Condition and the Flat-Plate Airfoil . Symmetrical Joukowski Airfoil . Circular-Arc Airfoil . Joukowski Airfoil . Schwarz-Christoffel Transformation . Source in a Channel . Flow Through an Aperture . Flow Past a Vertical Flat Plate Three-Dimensional Potential Flows . Velocity Potential . Stokes' Stream Function . Solution of the Potential Equation . Uniform Flow . Source and Sink . Flow Due to a Doublet . Flow Near a Blunt Nose . Flow Around a Sphere . Line-Distributed Source . Sphere in the Flow Field of a Source . Rankine Solids . D'Alembert's Paradox . Forces Induced by Singularities . Kinetic Energy of a Moving Fluid . Apparent Mass Surface Waves . The General Surface-Wave Problem . Small-Amplitude Plane Waves . Propagation of Surface Waves . Effect of Surface Tension . Shallow-Liquid Waves of Arbitrary Form . Complex Potential for Traveling Waves . Particle Paths for Traveling Waves . Standing Waves . Particle Paths for Standing Waves . Waves in Rectangular Vessels . Waves in Cylindrical Vessels . Propagation of Waves at an Interface VISCOUS FLOWS OF INCOMPRESSIBLE FLUIDS Exact Solutions . Couette Flow . Poiseuille Flow . Flow Between Rotating Cylinders . Stokes' First Problem . Stokes' Second Problem . Pulsating Flow Between Parallel Surfaces . Stagnation-Point Flow . Flow in Convergent and Divergent Channels . Flow Over a Porous Wall Low-Reynolds-Number Solutions . The Stokes Approximation . Uniform Flow . Doublet . Rotlet . Stokeslet . Rotating Sphere in a Fluid . Uniform Flow Past a Sphere . Uniform Flow Past a Circular Cylinder . The Oseen Approximation Boundary Layers . Boundary-Layer Thickness . The Boundary-Layer Equations . Blasius Solution . Falkner-Skan Solutions . Flow Over a Wedge . Stagnation-Point Flow . Flow in a Convergent Channel . Approximate Solution for a Flat Surface . General Momentum Integral . Karman-Pohlhausen Approximation . Boundary-Layer Separation . Stability of Boundary Layers Buoyancy-Driven Flows . The Boussinesq Approximation . Thermal Convection . Boundary-Layer Approximations . Vertical Isothermal Surface . Line Source of Heat . Point Source of Heat . Stability of Horizontal Layers COMPRESSIBLE FLOW OF INVISCID FLUIDS Shock Waves . Propagation of Infinitesimal Disturbances . Propagation of Finite Disturbances . Rankine-Hugoniot Equations . Conditions for Normal Shock Waves . Normal Shock-Wave Equations . Oblique Shock Waves One-Dimensional Flows . Weak Waves . Weak Shock Tubes . Wall Reflection of Waves . Reflection and Refraction at an Interface . Piston Problem . Finite-Strength Shock Tubes . Nonadiabatic Flows . Isentropic-Flow Relations . Flow Through Nozzles Multi-Dimensional Flows . Irrotational Motion . Janzen-Rayleigh Expansion . Small-Perturbation Theory . Pressure Coefficient . Flow Over a Wave-Shaped Wall . Pandtl-Glauert Rule for Subsonic Flow . Ackert's Theory for Supersonic Flows . Prandtl-Meyer Flow Appendix A. Vector Analysis Appendix B. Tensors Appendix C. Governing Equations Appendix D. Complex Variables Appendix E. Thermodynamics Index

Fundamental mechanics of fluids

The main feature is the representation of fluctuating lift behavior in terms of a proposed wake-oscillator. The primary purpose of the paper is to demonstrate the potential of the wake-oscillator concept for future studies. The elastically mounted cylinder is modeled as a second-order, linear, damped system. The aerodynamic lift force is proportional to the instantaneous value of a fluctuating lift coefficient. The instantaneous lift coefficient is derived from the response of a proposed lift-oscillator, whose characteristics are deduced from existing experimental data. This oscillator is self-excited, its natural frequency is proportional to wind speed, and it is subjected to a coupling term proportional to the transverse cylinder velocity.

Lift-Oscillator Model of Vortex-Induced Vibration

Measurements are presented of the fluctuating pressure recorded at a point 90° from the mean position of the forward stagnation point on a circular cylinder oscillating in a water flow. The aspect ratio of the cylinder was 9·5 and the turbulence level in the free-stream was 5·5%. The cylinder Reynolds number was 2·4 × 104 and the cylinder was forced to oscillate transverse to the main flow at amplitudes up to 1·33 cylinder diameters. The reduced velocity was varied over the range 3–18 and the experiments spanned the vortex-shedding lock-in range. Measurements of phase difference between pressure and displacement show that the maximum out-of-phase lift force occurs at an amplitude of about half a diameter. Good agreement is found between measurements on forced and freely oscillating cylinders. A simple potential-flow model gives reasonable predictions of the pressure fluctuations at the body frequency and at twice the body frequency at reduced velocities away from lock-in.

Pressure-fluctuation measurements on an oscillating circular cylinder

We report an experimental investigation of simple shear flow penetrating a model of a fibrous porous medium. The flow field is established between a stationary inner cylinder and a concentric outer cylinder rotating at a constant speed. The model medium is a regular array of rods which are oriented across the flow and which fill a fraction of the annular space between the cylinders. Rods with circular, square and triangular cross-sections are investigated, and the solid volume fraction of the arrays ranges from 0.01 to 0.16. With a viscous oil as the working fluid, the Reynolds number is much less than unity. Velocity measurements made using particle image velocimetry focus on the region around the edge of each array tested. The measurements reveal that eddies form between the two outermost circles of rods, for solid volume fractions above a minimum value which depends on rod shape. The velocity data are used to find the interfacial slip velocity and the average velocity at the interface between the porous medium and the outer shear flow

Velocity measurements of a shear flow penetrating a porous medium

Pressure losses and velocity distributions were measured for creeping flow through three model fibrous porous media. The three models consisted of square arrays of circular rods with solid volume fractions of 2.5, 5 and 10%. Measurements of flow resistances are in good agreement with theoretical predictions after wall effects are accounted for using Brinkman’s equation. Two-dimensional velocity vector maps were obtained in each array using particle image velocimetry. The velocity distributions are necessary for identifying non-Newtonian effects in flows with viscoelastic fluids.

I.G. Currie

Papers

Fundamental mechanics of fluids

Lift-Oscillator Model of Vortex-Induced Vibration

Pressure-fluctuation measurements on an oscillating circular cylinder

Velocity measurements of a shear flow penetrating a porous medium

Creeping flow through a model fibrous porous medium