🌪️ Wind Turbine BEM & Betz Limit Sizer
Calculate wind turbine aerodynamics with Blade Element Momentum (BEM) theory: power coefficient Cp, Betz limit, tip-speed ratio lambda, thrust load, and AEP.
⚡ Fortran 90 Engine
Double Precision (IEEE 754)
✓ ISO / ASME Validated
📊 Solver Telemetry
● ACTIVE
👁️ Consultations
41
⚡ Calculs faits
31
💾 Téléchargements
382
📦 Code Fortran
5.2 KB
📅 Mise en service
Jun 2026
⏱️ Latence
< 1 ms
🌪️ 3-Blade HAWT Rotor, Tower & Streamline Wake Deflection
Real-time visual simulation: Free-stream wind deceleration through disk, induction factor a, and wake expansion📝 Configuration & Presets
BEM Theory & Betz Formulation:
• Tip Speed Ratio: λ = (π · D · N / 60) / V∞
• Betz Theoretical Limit: Cp,max = 16/27 ≈ 59.26%
• Aero Power: Paero = ½ · ρ · A · V∞³ · Cp(λ, β) [MW]
• Rotor Thrust: T = ½ · ρ · A · V∞² · CT [kN].
• Tip Speed Ratio: λ = (π · D · N / 60) / V∞
• Betz Theoretical Limit: Cp,max = 16/27 ≈ 59.26%
• Aero Power: Paero = ½ · ρ · A · V∞³ · Cp(λ, β) [MW]
• Rotor Thrust: T = ½ · ρ · A · V∞² · CT [kN].
📊 Performance Results
📊 Output Summary
Turbine Electrical Rated Power
0.04 MW (40 kW)
Power Coeff Cp: 0.273 (Betz Limit: 59.3%) | TSR λ: 6.13
STALL / OFF-DESIGN OPERATION
Annual Energy Yield (AEP)
0.08 GWh/yr
Weibull c = 6.5 m/s
Rotor Aerodynamic Thrust
4.3 kN
Thrust Coeff CT = 0.273
Blade Tip Speed (Utip)
61.3 m/s
220.5 km/h
Rotor Swept Area
254 m²
Diameter = 18 m
📈 Electrical Power P (MW) vs Wind Speed V∞ (m/s)
📊 Aerodynamic Coeff Cp vs Tip Speed Ratio λ
================================================================= THERMOFLUIDCALC — WIND TURBINE BEM & BETZ REPORT ================================================================= Case Title : Small-Scale Community 50kW Wind Turbine Wind Resource : V = 10.0 m/s, rho = 1.225 kg/m3, Weibull c = 6.5 m/s Rotor Geometry : D = 18.0 m (Area = 254 m2), N = 65.0 rpm, Pitch = 0.0 deg ----------------------------------------------------------------- ELECTRICAL POWER (P_elec) : 0.040 MW (40.0 kW) Aerodynamic Power (P_aero) : 0.043 MW (Cp = 0.273 / Betz = 0.593) Tip Speed Ratio (TSR λ) : 6.13 (Tip Speed: 61.3 m/s) Rotor Total Thrust Load : 4.3 kN (Ct = 0.273) Estimated Annual Yield AEP : 0.08 GWh/year Operating Regime Status : STALL / OFF-DESIGN OPERATION =================================================================
📘 Calculation Methodology & Wind Aerodynamics Standards
Blade Element Momentum (BEM) Theory
BEM couples 1D momentum conservation across the rotor streamtube with 2D sectional airfoil lift and drag properties, resolving axial and angular flow induction factors $a$ and $a'$.
Betz Limit & Glauert Correction
Albert Betz proved that no wind turbine can capture more than 59.26% of kinetic energy. The Glauert correction handles high thrust states ($a > 0.33$) where momentum theory breaks down due to turbulent wake vortex mixing.
Key Engineering Assumptions
- IEC 61400-1 wind turbine design standards.
- Rayleigh/Weibull annual wind speed distribution.
- Widely used for onshore and offshore wind farm power rating and fatigue thrust analysis.