🌪️ 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

Turbomachinery

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👁️ Views 41

⚡ Solves 31

💾 Downloads 481 📦 Fortran Code 5.2 KB

📅 Released Jun 2026

⏱️ Latency < 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

🌊 NREL 5MW Offshore ⚡ Giant 8MW Deepwater 🏞️ Commercial 3MW Onshore 🏡 50kW Community Turbine

🌬️ Wind Resource & Atmospheric State

Rated Wind Speed V_∞ [m/s]:

Air Density ρ [kg/m³]:

Weibull Scale Parameter c [m/s]:

📐 Rotor Geometry & Kinematics

Rotor Diameter D [m]:

Rotor Speed N [rpm]:

Blade Pitch Angle β [deg]:

Number of Blades:

BEM Theory & Betz Formulation:
• Tip Speed Ratio: λ = (π · D · N / 60) / V_∞
• Betz Theoretical Limit: C_p,max = 16/27 ≈ 59.26%
• Aero Power: P_aero = ½ · ρ · A · V_∞³ · C_p(λ, β) [MW]
• Rotor Thrust: T = ½ · ρ · A · V_∞² · C_T [kN].

📊 Performance Results

📊 Output Summary
💾 Fortran Source

Turbine Electrical Rated Power

0.04 MW (40 kW)

Power Coeff C_p: 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 C_T = 0.273

Blade Tip Speed (U_tip) 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.

ThermoFluidCalc Engineering Report