Horizontal Axis Wind Turbines – Comprehensive Bullet Notes

Introduction

• Wind turbines convert kinetic energy of wind into electrical energy using lift generated by blades.
• Difference in pressure across blade surfaces produces lift > drag, rotating rotor → generator via gearbox or direct-drive.
• Horizontal Axis Wind Turbines (HAWTs) dominate global installations; Vertical Axis Wind Turbines (VAWTs) used for niche/urban.
• Betz limit: maximum theoretical power extraction $C_P^{max}=\frac{16}{27}\approx0.593$.
• Wind history: Persian panemones (7th C), Blyth 1887, Brush 1887, Smith–Putnam 1941.

Major Definitions & Preliminaries

• Tip-Speed Ratio (TSR) $\lambda=\frac{\omega R}{v_0}$ (angular velocity, radius, free-stream wind).
• Axial induction factor $a=\frac{v<em>0-U}{v</em>0}$.
• Power coefficient $C<em>P=\frac{P}{\tfrac12\rho A</em>R v_0^3}=4a(1-a)^2$.
• Cut-in / Rated / Cut-out speeds govern turbine operating regimes.
• Solidity $\sigma=\frac{Bc}{\pi R}$ (number of blades, chord, radius).
• Blockage Ratio for tunnels \frac{D}{W}\ (<0.5).

Wind Turbine Configurations

Horizontal-Axis (HAWT)

• 3-bladed upwind, gearbox or direct-drive, tubular tower.
• Gearless (permanent-magnet) avoids gearbox maintenance.
• Offshore sizes up to 8–12 MW, 80 m blades.

Vertical-Axis (VAWT)

• Darrieus “eggbeater”, Giromill, Savonius drag type.
• Pros: Omni-directional wind, generator at ground; Cons: lower $C_P$, higher torque ripple.
• Thick asymmetric NACA 6-series airfoils used to improve low-speed performance.

Blade Aerodynamics & Design

• Airfoil choice critical: flat-back at root (structural), sharp TE at tip (high TSR).
• Blade twist maintains optimal angle of attack along span (apparent wind variation).
• Higher TSR ⇒ smaller wake swirl & tip losses but noise/erosion rise.
• Design trade-off: aerodynamic efficiency vs structural stiffness & cost.
• CFD (Fluent, ANSYS) with SST k$-$\omega turbulence; mesh with y+≈1.

Actuator Disk Concept

• Uniform pressure drop across rotor; wake expands, velocity $U=v_0(1-2a)$; Betz derived.

Case Study 1 – Aerodynamics & Structural Analysis (HAWT Blade)

• Airfoils: S818 (root), S825 (mid), S826 (tip).
• CFD + FEM coupling; SST k$-$\omega, mesh with boundary layer.
• Blade length 43.2 m; design TSR 8; deflection tip 0.045 m at 12 m/s.
• Optimization highlights: outer 40 % span dominates torque.

Case Study 2 – Sensitive Parameters of HAWT Performance (CFD Review)

• Key influencing groups: Atmospheric wind statistics (Rayleigh, Weibull), blade shape (chord & twist), TSR, airfoil type, turbulence models.
• Tip-speed design: low $\lambda$ → high torque, high stress; high $\lambda$ → noise.
• Flat-back airfoils + vortex generators improve low-speed lift but raise drag/noise.
• CFD turbulence hierarchy: DNS (expensive) → LES → DES → RANS (k-ε, RNG, realizable, k-ω, SST, SA, Transition $\gamma-Re_\theta$).

Case Study 3 – Six-Blade Axial Turbine (Experimental)

• Variables: blade pitch 10°–80°, wind 2–5.6 m/s.
• Best modified power coefficient $C_{p}^* =0.57$ at 5.6 m/s & 80° pitch, but vibration high ⇒ avoid >3.8 m/s at 80°.

Case Study 4 – Blade Thickness in Asymmetric NACA 63-415 VAWT

• 2D URANS study, TSR range.
• Tested thickness ratio $t/c=0.22\to0.37$.
• Optimal $t/c=0.30$ yields $C_P=0.271$ at TSR≈2.4 for 6 m/s.
• Too thick (0.375) → large divergent suction side → flow separation & loss.

Case Study 5 – Flow Around a Single Turbine & Wake Physics

• Regions: Induction (upwind), Near-wake (0–2–4 D), Far-wake.
• Near-wake vortex structures: tip & root helicoidal vortices; hub vortex with Strouhal $St=fd/U_h$ 0.12–0.85.
• Far-wake self-similar Gaussian velocity deficit; wake growth $\sigma = kx$ where $k\propto I$.
• Wake meandering driven by large ABL eddies (>2 D); modelled by Dynamic Wake Meandering.
• Analytical models: Jensen top-hat, Frandsen, Bastankhah–Porté-Agel Gaussian ($\Delta \bar u / U<em>\infty = \left(1-\sqrt{1-C</em>T}/(1+2kx/D)^2\right)$).

Case Study 6 – AOC 15/50 Rotor Optimization

• 11 design variables (3 spanwise r/R, chord c, twist θ + cone ϕ, pitch α).
• Latin Hypercube DoE → Kriging RSM → NLPQL.
• Routine 1 (fixed length/chord): +7.6 % power at 8 m/s by twist at 40 % span (≈2.7°).
• Routine 2 (length +10 %, chord +7 %, twist +3°): +25 % torque (1069 Nm).
• Indicates power dominated by outer 30–40 % span.

Case Study 7 – Multi-Element Ducted Wind Turbine

• Duct + flap (NACA 4412) analysed via Panel, steady RANS, URANS.
• Parameters: radial gap $\zeta$ (% chord) & flap deflection $\theta$.
• Thrust coefficient $C_{T,M}$ rises with gap, falls with large deflection (separation).
• Optimal around $\zeta\approx5\%$, $\theta\approx10^{\circ}$ → power augmentation factor $r=\frac{C<em>P}{C</em>{P0}}\approx1.25$ (panel) –1.38 (RANS).
• Viscous separation at \theta>60^{\circ} → panel over-predicts.

Wake & Farm Interaction Summary

• Wake width grows linearly $\sigma= kx+\epsilon$. Empirical $k\approx0.38 I +0.004$.
• Turbulence intensity added: $\Delta I = \sqrt{I_w^2 - I^2}$; peak at ~2–4 D.
• Momentum flux high at wake edges, esp. upper due to shear.

Practical Implications & Design Guidelines

• Optimize outer blade geometry (chord, twist) for power; root mainly structural.
• Flat-back/thick airfoils useful for low-speed/structural but manage drag & noise.
• For VAWT low TSR, medium thickness (~30%) best; avoid excessive curvature.
• Analytical Gaussian wake model preferred for farm-scale layout & control; include turbulence-dependent growth.
• Ducted/augmented turbines: use small flap deflection & modest radial gap to boost thrust without separation.

Equations at a Glance

• Betz limit $C_P^{max}=0.593$
• TSR $\lambda=\omega R/v_0$
• Actuator Disk power $P=2\rho v<em>0 a(1-a) A</em>R$
• Gaussian wake $\Delta u/U<em>\infty = \left(1-\sqrt{1-C</em>T}\right)\exp\left(-\frac{r^2}{2\sigma^2}\right)$
• Power coeff. RSM objective $\max C_P(\mathbf{x})$ subject to geometry bounds.