Renewable energy · Year 4

Wind & airflow laboratory

An energy-conserving, lumped-parameter laboratory for engineering students—not a computational fluid dynamics solver.

AIRFLOW VELOCITY

10 m/s

AVAILABLE WIND POWER

1.92 kW

ELECTRICAL OUTPUT

654 W

TOTAL CONVERSION EFFICIENCY

34.0 %

Incoming airflow

Airflow control50%

0 m/sv = 0.2 × slider20 m/s

Rotor diametermAir densitykg/m³Generator efficiency0–1Power coefficient Cp0–0.593Blade pitchdegreesGenerator viscous loadN·m·s/radRotor position · visual only

Uniform incoming flow: rotor position changes the illustration, not wind power. Saved turbine parameters are shared.

Idealized wind turbine

Educational approximation

Rotor speed

765 rpm

Torque

9.61 N·m

Direction

Forward

Wind velocity & electrical power

Electrical output vs airflow sliderW

Air velocity vs airflow sliderm/s

Horizontal axis: slider 0–100%. These are calculated operating points, not measured time-series data.

Energy conversion & governing equations

Wind
1.92 kW

Mechanical
770 W

Electrical
654 W

A = π(D/2)² = 3.14 m²

Pavailable = ½ρA|v|³

Cp,effective = Cp × max(0, cos pitch)²

Pmechanical = Cp,effective × Pavailable

Pelectrical = η × Pmechanical

ω = sign(v)√(Pmechanical / (B + Bload))

T = Pmechanical / ω; B = 0.02 N·m·s/rad

ρ is air density; A is swept area; v is uniform wind speed; Cp is power coefficient bounded by the Betz limit 16/27; η is generator efficiency. The viscous equilibrium gives steady-state speed, not startup dynamics. Pitch is a declared cosine-squared approximation; Cp is not a blade-performance curve.

No CFD, turbulence, wake interaction, structural stress, or validated real turbine prediction. Reversing flow uses a symmetric ideal rotor assumption. Simulation does not certify hardware safety.