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What is BEMT?

The Buhl High-Induction Correction for Blade Element Momentum Theory Applied to Tidal Stream Turbines Dr. Ian Masters (Swansea University) Dr. Michael Togneri* (Swansea University) Marine Energy Research Group, Swansea University Singleton Park, Swansea, SA2 8PP, United Kingdom.

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What is BEMT?

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  1. The Buhl High-Induction Correction for Blade Element Momentum Theory Applied to Tidal Stream Turbines Dr. Ian Masters (Swansea University) Dr. Michael Togneri* (Swansea University) Marine Energy Research Group, Swansea UniversitySingleton Park, Swansea, SA2 8PP, United Kingdom

  2. What is BEMT? • Synthesis of two simple turbine models: • Stream tube & enclosed actuator disc • Hydrodynamic forces on 2D foils • Rotor disc enclosed in streamtube, with velocity and pressure variation. Image from Hansen, M“Aerodynamics of Wind Turbines”, Earthscan • Flow velocities for blade segment at radius r. Image from Burton, T et al, “Wind Energy Handbook”, John Wiley & Sons

  3. Characteristics of BEMT • Simpler problem than full CFD • Turbine effects on fluid ignored • Requires less computational power • Can obtain results much faster • Allows rapid investigation of wide range of cases • Simplifying assumptions: • Inflow/wake can be regarded as an enclosed streamtube • No wake mixing • Momentum change described by two parameters: • Axial induction factor (AIF, a), tangential induction factor (TIF, b)

  4. High induction state • AIF values in excess of 0.5 non-physical in classical BEMT Uwake = (1 – 2a)U∞ • Semi-empirical correction necessary • Must be validated against experiment

  5. High induction correction schemes • Graphs show high-induction corrections with and without tip/hub loss correction • Current model uses Buhl-derived formulation

  6. High induction correction schemes • Mathematical formulation straightforward • Momentum flux through annular element equated with hydrodynamic forces on corresponding portion of rotor blade: • f1: axial momentum flux; f2: axial blade forces; g1: tangential momentum flux; g2: tangential blade forces • Each term a function of AIF and TIF • Minimise (f1 – f2)2 + (g1 – g2)2 across (a,b)-space to determine solution • High induction correction simply modifies f1for high values of AIF (e.g., a > 0.4)

  7. High induction correction schemes • Classical Buhl formulation of axial force for a > ac: • Assumes perfect reversal of flow (i.e., CFa = 2) for a = 1 • Other values are plausible - e.g., 3D drag coefficient for a flat plate gives CFa(a = 1) = 1.3 • In general, denoting CFa(a = 1) by CFa1:

  8. Validation against experiment • Experimental data from work by Teddset al., Mason-Jones et al.

  9. Effects of HI correction on thrust • Uncorrected solution has higher thrust • More pronounced nearer the tip

  10. Effects of HI correction on thrust • Uncorrected solution has near-tip region of relatively high annular thrust • Coincides with the region where uncorrected AIF reaches physically meaningful limit

  11. HI correction for an existing rotor • 5o increase in rotor pitch moves rotor into HI regime

  12. HI correction for an existing rotor • 10o increase in pitch has more pronounced effect • Difficulties finding solution without HI correction

  13. Combining HI correction with tip/hub losses • HI correction has greater effect in conjunction with tip/hub losses • Losses lead to greater AIF values

  14. Summary • Classical BEMT does not deal with high induction, semi-empirical correction needed • Modified Buhl correction validated against experiment • Good agreement for power, less good for thrust • Correction works in conjunction with tip/hub losses • BEMT results for a high-induction rotor without HI correction not physically meaningful

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