Wind Turbine Components & Degrees of Freedom | DTU

Blade Element Momentum (BEM) theory is a mathematical model for describing wind turbine blade behavior. It combines blade element theory with momentum theory to calculate blade forces and performance. The theory is more rigorous than simple actuator disk models and is commonly used in software simulations for wind turbine design. BEM theory accounts for the complex interactions between blade geometry, wind conditions, and rotational dynamics.

The Aerodine module employs Blade Element Momentum (BEM) Theory to calculate aerodynamic loads on wind turbine blades. BEM combines Blade Element Theory, which divides the blade into discrete sections and computes aerodynamic forces using airfoil coefficient tables (lift, drag, and moment coefficients), with Actuator Disk Theory, which determines wind speed at the rotor disc based on upwind conditions. The blade speed is derived from Elastodyn's rotor speed, while incoming wind speed is obtained through actuator disk calculations. Correction factors can be applied to improve theoretical predictions. Airfoil parameters are specified in a dedicated blade file containing spanwise distribution of chord, curvature, angle of attack, and airfoil designations.

Blade Element Momentum Theory (BEMT) combines blade element analysis with momentum theory to calculate aerodynamic forces on wind turbine blades by analyzing 2D airfoil sections at various radial positions, resolving lift and drag into normal and tangential components to determine rotor torque and power through iterative solution of force and momentum equations involving non-dimensional parameters like tip speed ratio (λ) and solidity (σ).

This section presents the complete Blade Element-Momentum (BEM) theory framework. The actuator disk model provides momentum-based expressions: Thrust (dT) = ρ × A_ring × (u₂² - u₄²) and Torque (dQ) = ρ × A_ring × (u₂³ - u₄³) × (Ω/(1+a')). Velocities relate to induction factors via u₂ = u₁(1-a) and u₄ = u₁(1+a). Solidity (σ) = Bc/(2πR) represents blade area fraction. The BEM equations couple axial and tangential induction factors through normal force and torque equilibrium, involving lift and drag coefficients dependent on angle of attack. This creates a circular dependency requiring iterative solution.

Wind turbine performance is characterized by power coefficient (CP) and tip speed ratio (TSR). CP represents extraction efficiency, calculated as shaft power divided by available wind power. TSR is the ratio of blade tip velocity to free stream wind velocity. The relationship between TSR and wind speed is inverse: high wind speeds reduce TSR while low wind speeds increase it. Blade Element Momentum (BEM) theory combines 2D airfoil analysis with 1D momentum theory to predict performance. The method discretizes blades into sections analyzed using airfoil polars. BEM is inherently 2D and requires corrections for 3D spanwise flows. Polar extrapolation extends airfoil data beyond XFOIL simulation ranges using methods like Montgomery (flat plate assumption) or Viterna (trigonometric functions). Betz (1926) established the theoretical maximum power coefficient for horizontal axis wind turbines as 16/27 or approximately 59.59%. He defined four states in the fluid field: far upstream, two states near the rotor, and far downstream. By analyzing conservation of mass and energy, Betz derived that maximum power extraction occurs when downstream velocity equals one-third of upstream velocity. This limit applies to all wind turbines regardless of design, representing an absolute ceiling for steady-state energy extraction.

Aeroelastic phenomena in modern high-bypass turbofan engines present critical challenges due to lightweight composite blades, BLISK structures, and high aspect ratios, which reduce structural damping and increase susceptibility to flutter; effective analysis requires integrating experimental measurements (such as pressure-sensitive paint and ring tests) with numerical simulations (FSI methods) to understand complex interactions between unsteady aerodynamic forces and structural dynamics, including shock wave behavior, tip leakage flow, and non-synchronous vibrations that cannot be predicted by traditional methods alone.

Turbulent wind excitation on structures is modeled using a stationary Gaussian process characterized by mean wind velocity and power spectral density (PSD), where the PSD describes how wind energy is distributed across frequencies; the Davenport spectrum provides a practical model for this PSD, and aerodynamic admittance accounts for the size-dependent phase differences between pressure fluctuations on structures, enabling engineers to estimate dynamic forces and predict structural response under turbulent wind conditions.

Dynamic wind effects can cause structural responses that exceed those predicted by static analysis methods. The time-varying nature of wind loads means structures may experience higher forces and displacements than calculated assuming constant maximum loads. Aeroelastic phenomena occur when wind forces interact with structural flexibility to produce dynamic responses including vortex shedding, galloping, and flutter. Structural dynamics can be modeled using a mass-spring-damper system where mass represents inertia, spring represents stiffness, and damper represents energy dissipation. The natural frequency is the frequency at which a structure tends to vibrate when disturbed. When external forces contain energy at frequencies matching the structure's natural frequency, resonance occurs, potentially causing large-amplitude vibrations. Understanding natural frequencies is essential for avoiding resonant conditions in structural design.

Aeroelasticity involves the interaction between three force types: inertial forces (related to acceleration), aerodynamic forces (lift and drag), and elastic forces (structural deformation). Structures behave like springs with stiffness constants determining deformation under load. The center of twist is the critical point around which wings rotate under aerodynamic loading, and it can exist outside the wing's physical geometry. Understanding these fundamentals is essential for predicting how aircraft structures will behave under various flight conditions.

Advanced aeroelastic phenomena include vortex shedding lock-in causing dangerous resonance amplification, galloping producing self-excited oscillations growing with wind speed, and divergence torsion involving coupled vertical-rotational motions amplifying catastrophically. Critical structure vulnerabilities encompass flexible structures with low stiffness suffering significant damage, low-mass structures developing dangerous tension forces, transmission towers facing chain reaction failures, and structures with low aerodynamic damping unable to dissipate wind energy effectively. The Tacoma Narrows Bridge collapse exemplified divergence torsion where two modes interacted simultaneously. Group effect increases response when multiple structures alter local wind patterns, particularly affecting buildings with slenderness ratios exceeding 4 or 6.5.

Wind turbine gearboxes increase the low-speed rotation of the rotor to the high speeds required by the generator, typically with a ratio of 90:1 or higher. The gearbox contains multiple gear stages (typically planetary and helical gears) that multiply speed while transmitting torque. Modern gearboxes include sophisticated monitoring systems for temperature, vibration, and oil condition. Generators require cooling systems, typically using oil circulation or air flow through radiators, to maintain proper operating temperatures. Wind turbine generators use encoders to precisely measure the rotational position of the rotor shaft. The frequency converter (or inverter) is the heart of the power conversion system, performing rectification, DC link storage, and inversion. When the generator's rotational speed produces frequency below the grid frequency, the converter injects power into the rotor to increase the electrical output. When the generator's speed produces frequency above the grid frequency, the converter extracts power from the rotor to reduce the electrical output.

Wind turbine drivetrains convert low-speed, high-torque rotor input to high-speed, lower-torque generator output through mechanical components including the main shaft, gearbox (which may be step-up or step-down depending on application), high-speed shaft, and coupling; the generator converts this mechanical power to electrical power, with common configurations including induction generators (requiring grid connection and reactive power), synchronous generators with full conversion (expensive but flexible), and doubly fed induction generators (partial conversion, balancing cost and performance); direct drive turbines eliminate the gearbox entirely by using a massive generator with many pole pairs, trading generator cost for reduced maintenance complexity.

A generator system requires a mechanical power source (motor, wind, or water) to drive the generator rotor. The system uses a belt and pulley transmission where a small motor drives a large pulley (450mm diameter) connected to the generator. The motor operates at high RPM while the generator runs at low RPM (approximately 150-300 RPM). The pulley size difference creates the necessary speed reduction while maintaining torque. The generator produces three-phase AC power that passes through a rectifier before entering the inverter for grid injection.

The high-speed shaft transmits rotational speed and torque from the gearbox to drive the generator. The generator, mounted on top of the nacelle, converts mechanical energy into electrical energy. This final stage of the drivetrain transforms the increased rotational speed from the gearbox into usable electrical power that can be fed into the grid system.

This segment covers the complete mechanical power transmission chain from motor to generator. Key components include: (1) Gear boxes for speed reduction and torque increase, (2) Belt drives for flexible power transmission between shafts, (3) Proper alignment of rotating components to prevent vibration and wear, (4) Synchronization of rotating parts for efficient power transfer. The video demonstrates how these components work together to convert high-speed motor rotation into optimal generator speed for electricity generation.

Offshore wind foundations are categorized by water depth and site conditions. Fixed foundations include monopiles (single large-diameter cylinders driven into seabed, dominating the market at ~850 tons/unit), jackets (lattice structures for 30-60m depths), gravity bases, and suction buckets. Floating foundations include tension leg platforms (TLPs with taut mooring), semi-submersible platforms, and spar platforms (large-diameter floating cylinders). Monopiles were traditionally limited to 30m depths but are now being challenged at depths exceeding 70m. Floating solutions become necessary beyond 70m water depth where fixed foundations become economically unviable. Each foundation type requires specialized installation techniques and faces distinct structural challenges.

Offshore wind turbines use different foundation types depending on water depth and seabed conditions: monopile foundations (single large-diameter piles driven into seabed for shallow waters), jacket foundations (multi-legged steel structures for moderate depths), and floating foundations (for deep waters). Monopiles are simplest and most economical for depths up to about 30-50 meters. Jacket foundations provide stability in deeper waters with complex seabeds. Floating foundations use mooring systems for very deep or open ocean sites.

Offshore wind turbine foundations are selected based on water depth and seabed conditions: (1) Gravity base - large concrete block held by weight, suitable for 0-15m depth, (2) Section bucket - suction-based foundation, suitable for 0-30m depth, (3) Monopile - driven steel pile, suitable for 10-30m depth, (4) Jacket - lattice structure, suitable for 15-40m depth, (5) Floater - floating platform, suitable for depths over 50m. Monopiles are most commonly used due to low cost and reliability. Gravity bases are no longer used due to removal difficulties and scour problems. Jacket foundations are lattice structures requiring precise pile installation. Installation methods include grout connections (cement-like material, allows placement errors but risks settlement) and cup connections (conical steel cups that interlock, require precise placement but no grout needed).

Offshore structures use different foundation types based on water depth and application. Monopiles (freestanding caissons) represent 82% of offshore wind foundations and are used in shallow water (<50m). Tripods are used in very shallow water (<35m). Jacket structures (steel tubular) represent 95% of oil and gas platforms and are used in water depths up to 411m. In offshore wind, jackets represent about 10% of platforms and are used up to 60m depth. Pile dimensions vary significantly: oil and gas jacket piles can be 2.5m diameter and 140m long (L/D >30, long and flexible), while offshore wind monopiles have larger diameters for stiffness but shorter embedment (L/D 2-6, short and rigid).

Offshore wind turbine foundations differ significantly from onshore installations and depend on water depth and seabed conditions: (1) Monopile foundations are 3-8 meter wide steel piles driven into the seabed, suitable for 20-40 meter depths with hard to semi-hard seabeds; (2) Gravity-based foundations use heavy concrete caissons relying on sheer weight for stability, appropriate for shallow waters under 10 meters with clay and sandy soils; (3) Jacket or tripod foundations consist of hollow steel tube frames, suited for medium depths of 50-70 meters but presenting substantial logistical challenges.