Report

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 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 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) 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 High induction correction schemes 2.5 BEMT CFa-a curve Spera-corrected C Fa-a curve Glauert-corrected C Fa-a curve 2 Buhl-corrected CFa-a curve CFa 1.5 1 0.5 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 a • Graphs show high-induction corrections with and without tip/hub loss correction • Current model uses Buhl-derived formulation 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 f1 for high values of AIF (e.g., a > 0.4) 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 : Validation against experiment • Experimental data from work by Tedds et al., Mason-Jones et al. Effects of HI correction on thrust • Uncorrected solution has higher thrust • More pronounced nearer the tip 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 HI correction for an existing rotor • 5o increase in rotor pitch moves rotor into HI regime HI correction for an existing rotor • 10o increase in pitch has more pronounced effect • Difficulties finding solution without HI correction Combining HI correction with tip/hub losses • HI correction has greater effect in conjunction with tip/hub losses • Losses lead to greater AIF values 0.9 0.8 0.7 0.6 CFa 0.5 0.4 0.3 0.2 Uncorrected curve HI correction only Tip/hub loss correction only Both corrections 0.1 0 0 1 2 3 4 TSR 5 6 7 8 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