What Is the Wind Turbine Blade Element Momentum (BEM) Calculator?
BEM theory couples momentum conservation across rotor annular streamtubes with 2D airfoil aerodynamic lift and drag.
How Does the Wind Turbine Blade Element Momentum (BEM) Calculator Work?
Iteratively updates axial induction a and swirl induction a_prime until blade forces match fluid momentum changes.
Wind Turbine Blade Element Momentum (BEM) Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
a = rac{1}{ rac{4 sin^2(phi)}{sigma C_n} + 1}, quad an(phi) = rac{1 - a}{(1 + a') lambda_r}
BEM iterative induction and inflow angle governing equations.
How to Use the Wind Turbine Blade Element Momentum (BEM) Calculator
- Enter rotor tip-speed ratio, radial span fraction (r/R), local blade solidity, and airfoil lift coefficient Cl.
Step-by-Step Example Calculation
3 MW Utility Wind Turbine at 70% Span
Input Values:
tipSpeedRatioLambda:7.5
radialFractionR:0.7
bladeSoliditySigma:0.075
liftCoeffCl:1.15
Worked Steps: Axial induction a = 0.312, Angular induction a' = 0.0078, Inflow angle phi = 7.4°, Thrust coefficient Ct = 0.859.
Understanding Your Result
Displays axial induction factor a, swirl induction a_prime, relative inflow angle phi, and local thrust coefficient Ct.
Factors That Affect the Result
- Axial induction near Betz optimum (a = 0.333) maximizes aerodynamic power extraction.
When Should You Use This Calculator?
- Aerodynamic blade design, aerodynamic twist/chord distribution optimization, and turbine power curve modeling.
Assumptions & Limitations
- Assumes steady 2D streamtubes without spanwise flow; applies momentum theory.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard iterative BEM aerodynamic formulation.