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C OHERENT A PPLICATION T HREAD S

CATs. C OHERENT A PPLICATION T HREAD S. Wind Turbines. Supplemental Learning Module ME 303 Fluid Mechanics Control Volume Analysis and the Betz Limit. Don Wroblewski Associate Professor, Mechanical Engineering Associate Chair, Aerospace Engineering

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C OHERENT A PPLICATION T HREAD S

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  1. CATs COHERENT APPLICATION THREADS Wind Turbines Supplemental Learning Module ME 303 Fluid Mechanics Control Volume Analysis and the Betz Limit Don Wroblewski Associate Professor, Mechanical Engineering Associate Chair, Aerospace Engineering Undergraduate Program

  2. BETZ LIMIT SETUP Wind Speed downstream of rotor Streamtube Wind Speed through rotor Undisturbed Wind Speed Force exerted by rotor on wind V2 F V V1 A1 Rotor area A A2 P Power extracted at rotor

  3. BETZ LIMIT ASSUMPTIONS • Wind velocity is always axial (normal to flow areas) • Steady State, Uniform Flow • Incompressible, adiabatic flow • Ideal rotor • Zero mass • Zero drag • No Wake V2 F V V1 A1 A A2 P

  4. BETZ LIMIT ANALYSIS • Apply following to control volume • Conservation of mass: relates V’s to A’s • Momentum equation: relates F to V’s and A’s • Energy equation: relates P to V’s and A’s • Other: P=VF Control volume V2 F V V1 A1 A A2 P

  5. Betz Limit Results Coefficient of Performance Coefficient of Performance vs Velocity Ratio V2 V V1

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